Webb damaged the rotator cuff in his shoulder after coming off the bench in England's Six Nations win over France.
And with the 25-year-old leaving Adams Park in the summer to join Bath, he will not get the chance to play for Wasps again.
However, the hooker has vowed to continue to work hard behind the scenes for the club as they continue their fight against relegation.
"I'm really disappointed that I won't play for Wasps again and it's a frustrating way to end my playing career with the club," Webber told the club's official website.
"I will absolutely be around the club from now until the end of the season and will do anything I can to help the squad in the final run-in."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.