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.
(Reporting by Martyn Herman; editing by Justin Palmer)
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