Skrtel escaped punishment at the time because the stoppage-time incident was missed by the match officials but video footage resulted in him being charged with violent conduct by the Football Association.
The Slovakian had denied the charge but was found guilty by an Independent Regulatory Commission hearing.
Skrtel will miss the clash at Arsenal on April 4, as well as the FA Cup semi-final against Blackburn Rovers and the league game at home to Newcastle United.
It is a blow to Liverpool's top-four ambitions, especially as captain Steven Gerrard is also suspended for three matches after being red-carded for a stamp 38 seconds after coming on as a substitute against United.
Image: Liverpool's Martin Skrtel challenges Manchester United's David De Gea
Photograph: Phil Noble/Reuters
Liverpool's Skrtel charged with violent conduct
EPL PHOTOS: Chelsea beat valiant Hull to go six points clear
Cisse and Evans handed hefty bans for spitting
Falcao may quit Manchester United at end of season
Mata strikes twice as United down 10-man Liverpool