Wickham went unpunished at the time as the incident was not seen by the match officials, but an Independent Regulatory Commission hearing found him guilty of violent conduct after viewing video footage.
Vertonghen was substituted shortly after the 69th minute incident with a knee injury sustained when he fell awkwardly.
Wickham will miss Palace's FA Cup fourth round clash at home to Stoke City on Saturday plus league games against visitors Bournemouth and at Swansea City.
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(Reporting by Martyn Herman; editing by Ken Ferris)
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