The Cameroon international, who joined QPR from Marseille last summer, appeared to contact Joey Barton and ask if he fancied swapping clubs.
Mbia denied sending the messages, claiming someone got hold of his login and password, but QPR's head of media and communications Ian Taylor confirmed in a statement that the 26-year-old had been fined.
He said: "The club has concluded its investigation following a series of tweets which appeared on Stephane Mbia's official Twitter account.
"Stephane has stressed to the club that he is not responsible for the Tweets. However the club is of the view that every player that has a Twitter account is ultimately responsible for what appears on it.
"As a result, Stephane has been fined and warned in relation to his future conduct. The club will be making no further comment."