The operation in Basel lasted 90 minutes and was without complications, the agency added.
Cancellara suffered multiple fractures to his collar bone during Sunday's race, which was won by Belgium's Tom Boonen for a record-equalling third time.
The Swiss Olympic time-trial champion, who won in 2010 and was one of the pre-race favourites for the second one-day classic of the season, fell 62km from the finish.
SportInformation said that he could resume training soon but his classics season, which saw him tipped for a win in the Paris-Roubaix race next Sunday, is likely to have come to a premature end.
RadioShack-Nissan team doctor Andreas Goesele also said he was optimistic about the rider's recovery and that he could even be back in the saddle and training from Tuesday.
The Swiss daily Le Matin quoted the sporting director of RadioShack, Dirk Demol, as saying that Cancellara will return to competition in the Tour of Bavaria on May 23-27 or for the Tour of Luxembourg (May 30-June 3).