Silva was originally charged with misconduct by the FA in October after the Portuguese tweeted an image of a young Mendy alongside an image of the brand mascot of Spanish confectionery brand Conguitos, with the caption "Guess who?", on September 22.
Silva then deleted the tweet, before posting a new one that read: "Can't even joke with a friend these days..."
The FA said the tweet had committed an "aggravated breach" of the football body's rules and means he now misses City's Premier League fixture against Chelsea on November 23.
Fabinho, Mohamed Salah and Sadio Mane were on target for the Merseysiders as Bernardo Silva scored City's consolation.
City will therefore by without Silva for this weekend, with the player picking up a one-match suspension.
Manchester City defender Benjamin Mendy issued a supporting statement saying he did not take offence.
In their commission report, the FA also explain that the player did not intend for the tweet to be racist or insulting.
And after coming in for plenty of criticism, the Portugal global then later tweeted: 'Can't even joke with a friend these days. you guys'.
They added: "However, this was not a private jocular communication between two friends, The post was on a social media platform exposed to the 600,000 followers of a high-profile and well-respected professional footballer".
The English Football Association (FA) has also instructed the Portuguese global to complete face-to-face education after he admitted his post was insulting and improper and brought the game into disrepute.
Raheem Sterling made headlines this week following a bust-up with Liverpool's Joe Gomez on global duty.