Fernandinho was sent off for a challenge on Burnley winger Johann Gudmundsson in the 32nd in City's 2-1 win on Monday, and City's appeal against the sending off has been turned down.
The Brazilian went in heavily on the Iceland international and the City midfielder will now be unavailable for the next four games after receiving his second red card in the Premier League this season.
Fernandinho will now miss Man City's FA Cup tie with West Ham on Friday, along with Premier League clashes against Everton, Tottenham and West Ham.