The 24-year-old was sent off for the incident, which came in the 49th minute of the Hammers' 2-0 defeat at the DW Stadium.
Masuaku apologised for his actions in a statement released on Sunday, admitting it was a "totally unacceptable" reaction that was "out of character".
The Football Association confirmed the former Olympiakos man will be suspended for six matches, meaning he will sit out games against Crystal Palace, Brighton and Hove Albion, Watford, Liverpool, Swansea City and Burnley, returning for the home game against Manchester United on March 18.
Manager David Moyes described Masuaku's conduct as "despicable" and confirmed he would face additional punishment from the club.
"He will get something off us," Moyes said after the match.
"Let me not hide behind it. The referee didn't see it, he was influenced by the players, but it was the right decision [to send Masuaku off].
"We gave him a chance, we like him, he's a good boy around the club and I've enjoyed him. It is out of character."