But Simpson, who was hurt during Wasps' Aviva Premiership victory over London Welsh three days ago, is unlikely to require surgery.
"Thankfully it doesn't look like it needs an operation," Wasps rugby director David Young said.
"At the moment he is looking at around three-four weeks of rehab, which is much better than we first thought."
Simpson, 24, was capped by England during the World Cup in New Zealand last year.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
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.
