diff --git a/src/wp-admin/includes/file.php b/src/wp-admin/includes/file.php
index 152a1e2f21..40059273ba 100644
--- a/src/wp-admin/includes/file.php
+++ b/src/wp-admin/includes/file.php
@@ -1241,6 +1241,24 @@ function download_url( $url, $timeout = 300, $signature_verification = false ) {
 		}
 	}
 
+	$mime_type = wp_remote_retrieve_header( $response, 'content-type' );
+	if ( $mime_type && 'tmp' === pathinfo( $tmpfname, PATHINFO_EXTENSION ) ) {
+		$valid_mime_types = array_flip( get_allowed_mime_types() );
+		if ( ! empty( $valid_mime_types[ $mime_type ] ) ) {
+			$extensions     = explode( '|', $valid_mime_types[ $mime_type ] );
+			$new_image_name = substr( $tmpfname, 0, -4 ) . ".{$extensions[0]}";
+			if ( 0 === validate_file( $new_image_name ) ) {
+				if ( rename( $tmpfname, $new_image_name ) ) {
+					$tmpfname = $new_image_name;
+				}
+
+				if ( ( $tmpfname !== $new_image_name ) && file_exists( $new_image_name ) ) {
+					unlink( $new_image_name );
+				}
+			}
+		}
+	}
+
 	$content_md5 = wp_remote_retrieve_header( $response, 'Content-MD5' );
 
 	if ( $content_md5 ) {
diff --git a/tests/phpunit/tests/admin/includesFile.php b/tests/phpunit/tests/admin/includesFile.php
index 943cabb7c0..20ced72821 100644
--- a/tests/phpunit/tests/admin/includesFile.php
+++ b/tests/phpunit/tests/admin/includesFile.php
@@ -389,4 +389,78 @@ class Tests_Admin_IncludesFile extends WP_UnitTestCase {
 
 		return $response;
 	}
+
+	/**
+	 * Test that `download_url()` properly handles setting the file name when set using
+	 * the content type header on URLs with no file extension.
+	 *
+	 * @dataProvider data_download_url_should_use_the_content_type_header_to_set_extension_of_a_file_if_extension_was_not_determined
+	 *
+	 * @covers ::download_url
+	 * @ticket 54738
+	 *
+	 * @param string $filter A callback containing a fake Content-Type header.
+	 * @param string $ext The expected file extension to match.
+	 */
+	public function test_download_url_should_use_the_content_type_header_to_set_extension_of_a_file_if_extension_was_not_determined( $filter, $extension ) {
+		add_filter( 'pre_http_request', $filter );
+
+		$filename = download_url( 'url_with_content_type_header' );
+		$this->assertStringEndsWith( $extension, $filename );
+		$this->assertFileExists( $filename );
+		$this->unlink( $filename );
+	}
+
+	/**
+	 * Data provider for test_download_url_should_use_the_content_type_header_to_set_extension_of_a_file_if_extension_was_not_determined
+	 *
+	 * @see test_download_url_should_use_the_content_type_header_to_set_extension_of_a_file_if_extension_was_not_determined()
+	 * @test
+	 * @ticket 54738
+	 *
+	 * @return Generator
+	 */
+	public function data_download_url_should_use_the_content_type_header_to_set_extension_of_a_file_if_extension_was_not_determined() {
+		yield 'Content-Type header in the response' => array(
+			function () {
+				return array(
+					'response' => array(
+						'code' => 200,
+					),
+					'headers'  => array(
+						'content-type' => 'image/jpeg',
+					),
+				);
+			},
+			'.jpg',
+		);
+
+		yield 'Invalid Content-Type header' => array(
+			function () {
+				return array(
+					'response' => array(
+						'code' => 200,
+					),
+					'headers'  => array(
+						'content-type' => '../../filename-from-content-disposition-header.txt',
+					),
+				);
+			},
+			'.tmp',
+		);
+
+		yield 'Valid content type but not supported mime type' => array(
+			function () {
+				return array(
+					'response' => array(
+						'code' => 200,
+					),
+					'headers'  => array(
+						'content-type' => 'image/x-xbm',
+					),
+				);
+			},
+			'.tmp',
+		);
+	}
 }