The FA also severely reprimanded Wenger and warned him not to repeat the offense.
A disciplinary panel found the Frenchman guilty of improper conduct after his team's 2-0 loss to United in a Premier League game on Oct. 24.
"We all know him he can only cheat people Wenger said of Van Nistelrooy in a post-match television interview.
Wenger contested the charge but did not appear at Thursday's FA disciplinary hearing.
His case was put by legal representatives and the club issued a statement afterwards saying he did not plan to appeal against the verdict or the punishment.
"Now is the time to move on Wenger said in the statement. "We have an important match coming up and all my thoughts are focused on our preparations for the visit to Portsmouth on Sunday."
The Old Trafford game marked Arsenal's first defeat in 50 league games and led to acrimonious scenes as the players and team officials left the field.
Man U manager Alex Ferguson was pelted with soup and pizza during the scuffles.
Van Nistelrooy who has had repeated flare-ups with Arsenal players on the field served a three-game ban for kicking Gunners defender Ashley Cole in the knee during the game. The incident was not spotted by the referee but the FA charged him with serious foul play.