Jackson should recover in time to be available for the 2015 World Cup tournament next September.
"We are all incredibly disappointed for Ruaridh, who has made such an impact since joining Wasps this season," Wasps director of rugby Dai Young said.
"He has impressed me during training, both with his skill level and his attitude, and it's a real blow to lose him.
"Our medical team will be monitoring Ruaridh carefully and supporting him through this frustrating period. Professional sport is cruel at times and this is certainly one of those times."
Jackson made his debut for Scotland against New Zealand in November 2010 and has appeared in 25 tests overall, including 12 as a replacement.
(Reporting By Tim Collings, editing by Pritha Sarkar)
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