diff --git src/wp-includes/formatting.php src/wp-includes/formatting.php
index 46d9a90..153b9db 100644
--- src/wp-includes/formatting.php
+++ src/wp-includes/formatting.php
@@ -1725,7 +1725,8 @@ function remove_accents( $string ) {
  * operating systems and special characters requiring special escaping
  * to manipulate at the command line. Replaces spaces and consecutive
  * dashes with a single dash. Trims period, dash and underscore from beginning
- * and end of filename.
+ * and end of filename. It is not guaranteed that this function will return a
+ * filename that is allowed to be uploaded.
  *
  * @since 2.1.0
  *
@@ -1750,6 +1751,14 @@ function sanitize_file_name( $filename ) {
 	$filename = preg_replace( '/[\r\n\t -]+/', '-', $filename );
 	$filename = trim( $filename, '.-_' );
 
+	if ( false === strpos( $filename, '.' ) ) {
+		$mime_types = wp_get_mime_types();
+		$filetype = wp_check_filetype( 'test.' . $filename, $mime_types );
+		if ( $filetype['ext'] === $filename ) {
+			$filename = 'unnamed-file.' . $filetype['ext'];
+		}
+	}
+
 	// Split the filename into a base and extension[s]
 	$parts = explode('.', $filename);
 
diff --git tests/phpunit/tests/formatting/SanitizeFileName.php tests/phpunit/tests/formatting/SanitizeFileName.php
index 8927fec..d26b871 100644
--- tests/phpunit/tests/formatting/SanitizeFileName.php
+++ tests/phpunit/tests/formatting/SanitizeFileName.php
@@ -56,4 +56,15 @@ class Tests_Formatting_SanitizeFileName extends WP_UnitTestCase {
 	function test_replaces_percent_sign() {
 		$this->assertEquals( 'a22b.jpg', sanitize_file_name( 'a%22b.jpg' ) );
 	}
+
+	function test_replaces_unnammed_file_extensions() {
+		// Test filenames with both supported and unsupported extensions.
+		$this->assertEquals( 'unnamed-file.exe', sanitize_file_name( '_.exe' ) );
+		$this->assertEquals( 'unnamed-file.jpg', sanitize_file_name( '_.jpg' ) );
+	}
+
+	function test_replaces_unnammed_file_extensionless() {
+		// Test a filenames that becomes extensionless.
+		$this->assertEquals( 'no-extension', sanitize_file_name( '_.no-extension' ) );
+	}
 }