The Portuguese dislocated his shoulder in the Hammers' last Premier League encounter against Arsenal and it was decided keyhole surgery would be the best treatment with Vaz Te undergoing the operation on Monday night.
Boss Sam Allardyce told the club's official website: "We think we've chosen the best option to strengthen the shoulder and get him back as quickly as we can."
Vaz Te's absence gives West Ham's fringe midfielders a chance to prove their worth.
"We've got some good players ready to step up in place. Matt Taylor has been there and there are others in the squad that haven't quite played as much such as Gary O'Neil," Allardyce added.
"Whichever option we pick it's up to them to step up to the mark. They need to provide the attacking opportunities that we need."