The Uruguay international has been suspended for one game and fined £20,000 after accepting a Football Association charge of improper conduct relating to a one-fingered sign aimed at home supporters following Liverpool's 1-0 defeat at Craven Cottage.
Suarez already has the prospect of an eight-match ban hanging over him after being found guilty of misconduct for using insulting words to Manchester United's Patrice Evra which contained reference to the defender's colour.
That suspension is currently on hold as Liverpool have 14 days to appeal once they have received the written judgement from the independent commission which heard the case.