Mitrovic appeared to catch West Ham’s Manuel Lanzini with an elbow during Newcastle’s 3-0 win on Saturday in an incident that was not seen by referee Neil Swarbrick or his assistants.
The FA’s disciplinary committee reviewed the clash on video and Mitrovic was hit with the charge.
The Serbia international will miss Newcastle’s Premier League games with Swansea, Stoke and Brighton and will be eligible to return for the home clash with Liverpool on October 1.
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