The tie kept United in the second spot with 45 points, 13 after runway leaders Chelsea while the fading Gunners remained fifth on 34 with one match in hand.
The hosts looked better in the first-half as they packed the midfield with players with captain Thierry Henry often returning to the midfield to feed wingers Robert Pires and Jose Antonio Reyes.
Belarusian midfielder Alexander Hleb missed the first chance after just three minutes when he failed to connect with Pires' inch-perfect cross from the right flank.
Seven minutes later, Cesc Fabregas came close from breaking the deadlock with a stinging shot from the edge of the area but his effort went inches wide.
Henry made his first try on the goal in the 31st minute when he stepped up to deliver a curling free-kick that sailed over the bar and just missed the top corner.
With one minute remaining in the first period, Cristiano Ronaldo squandered a rare scoring opportunity when he fired high instead of poking into the empty net after Ruud Van Nistelrooy's initial effort was blocked by Jens Lehman.
The game got more tied after the break but Manchester looked better and managed to threaten Arsenal's net thanks to the energetic Ronaldo who outpaced left-back Pascal Cygan more than once.
The visitors were on the verge of scoring in the dying second but Nistelrooy failed to deliver on more than one occasion as the game ended in a goalless draw.