diff --git a/src/DateUtils.ts b/src/DateUtils.ts
index a6a8caa946..9116a8047d 100644
--- a/src/DateUtils.ts
+++ b/src/DateUtils.ts
@@ -102,6 +102,21 @@ export function formatFullDate(date: Date, showTwelveHour = false, showSeconds =
     });
 }
 
+/**
+ * Formats dates to be compatible with attributes of a `<input type="date">`. Dates
+ * should be formatted like "2020-06-23" (formatted according to ISO8601)
+ *
+ * @param date The date to format.
+ * @returns The date string in ISO8601 format ready to be used with an `<input>`
+ */
+export function formatDateForInput(date: Date): string {
+    const year = `${date.getFullYear()}`.padStart(4, "0");
+    const month = `${date.getMonth() + 1}`.padStart(2, "0");
+    const day = `${date.getDate()}`.padStart(2, "0");
+    const dateInputValue = `${year}-${month}-${day}`;
+    return dateInputValue;
+}
+
 export function formatFullTime(date: Date, showTwelveHour = false): string {
     if (showTwelveHour) {
         return twelveHourTime(date, true);
diff --git a/src/components/views/messages/JumpToDatePicker.tsx b/src/components/views/messages/JumpToDatePicker.tsx
index fa13235809..8bfcebb3ae 100644
--- a/src/components/views/messages/JumpToDatePicker.tsx
+++ b/src/components/views/messages/JumpToDatePicker.tsx
@@ -19,6 +19,7 @@ import React, { useState, FormEvent } from "react";
 import { _t } from "../../../languageHandler";
 import Field from "../elements/Field";
 import { RovingAccessibleButton, useRovingTabIndex } from "../../../accessibility/RovingTabIndex";
+import { formatDateForInput } from "../../../DateUtils";
 
 interface IProps {
     ts: number;
@@ -27,12 +28,9 @@ interface IProps {
 
 const JumpToDatePicker: React.FC<IProps> = ({ ts, onDatePicked }: IProps) => {
     const date = new Date(ts);
-    const year = date.getFullYear();
-    const month = `${date.getMonth() + 1}`.padStart(2, "0");
-    const day = `${date.getDate()}`.padStart(2, "0");
-    const dateDefaultValue = `${year}-${month}-${day}`;
+    const dateInputDefaultValue = formatDateForInput(date);
 
-    const [dateValue, setDateValue] = useState(dateDefaultValue);
+    const [dateValue, setDateValue] = useState(dateInputDefaultValue);
     const [onFocus, isActive, ref] = useRovingTabIndex<HTMLInputElement>();
 
     const onDateValueInput = (ev: React.ChangeEvent<HTMLInputElement>): void => setDateValue(ev.target.value);
@@ -49,6 +47,9 @@ const JumpToDatePicker: React.FC<IProps> = ({ ts, onDatePicked }: IProps) => {
                 type="date"
                 onInput={onDateValueInput}
                 value={dateValue}
+                // Prevent people from selecting a day in the future (there won't be any
+                // events there anyway).
+                max={formatDateForInput(new Date())}
                 className="mx_JumpToDatePicker_datePicker"
                 label={_t("Pick a date to jump to")}
                 onFocus={onFocus}
diff --git a/test/components/views/messages/JumpToDatePicker-test.tsx b/test/components/views/messages/JumpToDatePicker-test.tsx
new file mode 100644
index 0000000000..c75c6d8ffd
--- /dev/null
+++ b/test/components/views/messages/JumpToDatePicker-test.tsx
@@ -0,0 +1,41 @@
+/*
+Copyright 2021 The Matrix.org Foundation C.I.C.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+import React from "react";
+import { render } from "@testing-library/react";
+
+import JumpToDatePicker from "../../../../src/components/views/messages/JumpToDatePicker";
+
+describe("JumpToDatePicker", () => {
+    const nowDate = new Date("2021-12-17T08:09:00.000Z");
+    beforeEach(() => {
+        // Set a stable fake time here so the test is always consistent
+        jest.useFakeTimers();
+        jest.setSystemTime(nowDate.getTime());
+    });
+
+    afterAll(() => {
+        jest.useRealTimers();
+    });
+
+    it("renders the date picker correctly", () => {
+        const { asFragment } = render(
+            <JumpToDatePicker ts={new Date("2020-07-04T05:55:00.000Z").getTime()} onDatePicked={() => {}} />,
+        );
+
+        expect(asFragment()).toMatchSnapshot();
+    });
+});
diff --git a/test/components/views/messages/__snapshots__/JumpToDatePicker-test.tsx.snap b/test/components/views/messages/__snapshots__/JumpToDatePicker-test.tsx.snap
new file mode 100644
index 0000000000..02d5d3a337
--- /dev/null
+++ b/test/components/views/messages/__snapshots__/JumpToDatePicker-test.tsx.snap
@@ -0,0 +1,41 @@
+// Jest Snapshot v1, https://goo.gl/fbAQLP
+
+exports[`JumpToDatePicker renders the date picker correctly 1`] = `
+<DocumentFragment>
+  <form
+    class="mx_JumpToDatePicker_form"
+  >
+    <span
+      class="mx_JumpToDatePicker_label"
+    >
+      Jump to date
+    </span>
+    <div
+      class="mx_Field mx_Field_input mx_JumpToDatePicker_datePicker"
+    >
+      <input
+        id="mx_Field_1"
+        label="Pick a date to jump to"
+        max="2021-12-17"
+        placeholder="Pick a date to jump to"
+        tabindex="-1"
+        type="date"
+        value="2020-07-04"
+      />
+      <label
+        for="mx_Field_1"
+      >
+        Pick a date to jump to
+      </label>
+    </div>
+    <button
+      class="mx_AccessibleButton mx_JumpToDatePicker_submitButton mx_AccessibleButton_hasKind mx_AccessibleButton_kind_primary"
+      role="button"
+      tabindex="-1"
+      type="submit"
+    >
+      Go
+    </button>
+  </form>
+</DocumentFragment>
+`;
diff --git a/test/utils/DateUtils-test.ts b/test/utils/DateUtils-test.ts
index aa8cf2d994..9b1fe4d870 100644
--- a/test/utils/DateUtils-test.ts
+++ b/test/utils/DateUtils-test.ts
@@ -19,6 +19,7 @@ import {
     formatRelativeTime,
     formatDuration,
     formatFullDateNoDayISO,
+    formatDateForInput,
     formatTimeLeft,
     formatPreciseDuration,
     formatLocalDateShort,
@@ -126,6 +127,15 @@ describe("formatFullDateNoDayISO", () => {
     });
 });
 
+describe("formatDateForInput", () => {
+    it.each([["1993-11-01"], ["1066-10-14"], ["0571-04-22"], ["0062-02-05"]])(
+        "should format %s",
+        (dateString: string) => {
+            expect(formatDateForInput(new Date(dateString))).toBe(dateString);
+        },
+    );
+});
+
 describe("formatTimeLeft", () => {
     it.each([
         [0, "0s left"],