The Italian Football Federation (FICG) confirmed on Wednesday that the Netherlands international's appeal against the sanction has been rejected.
He was adjudged to be guilty of simulation in an incident with defender Wallace to win Roma a penalty that was subsequently scored by Daniele De Rossi.
It was ruled that the 27-year-old's "unnatural turn and relative fall to the floor could in no instance be caused by the attempts by Lazio's player Wallace to intervene" - an act that represented "seriously unsporting behaviour".
Strootman had been successful in appealing a ban for simulation in another match against Lazio last December, but this time he has failed to get a reprieve.
Luciano Spalletti's men play Milan at San Siro this Sunday before hosting Juventus at Stadio Olimpico on May 14, with Strootman not in line to return until the trip to Chievo on May 21.
Roma are second in Serie A, nine points behind leaders Juve and one clear of Napoli in third.