The news is a major blow to the player, who may now miss his side's opening match in the Heineken Cup against Biarritz Olympique on October 24.
Lewsey has had two pins inserted in his hand after X-rays confirmed a fracture, sustained in Saturday's defeat to Sale.
With his hand wrapped in a protective cast, he will miss Wasps' forthcoming Zurich Premiership matches.
The 27-year-old should be back to full fitness in time for England's three November internationals.
Lewsey is the latest international player to join Wasps' mounting injury list as the champions strive to recover from a disappointing start to the Premiership.
England centre Stuart Abbott is likely to be absent until the end of November as he recovers from a shoulder operation.
Lock Simon Shaw's neck strain has not healed as quickly as hoped and he will be out for another fortnight.
Centre Fraser Waters hopes to return from an ankle operation in the next fortnight but former All Blacks prop Craig Dowd (Achilles) will be sidelined for another six weeks.Welsh scrum-half Rob Howley will not return from a wrist operation until November, while lock Martin Purdy's dislocated shoulder will keep him out until January.