Defender Vermaelen was ordered off shortly before half-time for bringing down Guillermo Franco inside the penalty area.
Arsenal were leading 1-0 and went on to win 2-0, with West Ham's Alessandro Diamanti missing the penalty which followed Vermaelen's dismissal.
A statement from the Football Association on Arsenal's website said: "The FA has received a claim for wrongful dismissal from Arsenal defender Thomas Vermaelen.
"Vermaelen was shown a red card for denying an obvious goalscoring opportunity during Arsenal's match against West Ham United on Saturday 20 March.
"A regulatory commission will hear the claim on Tuesday 23 March."