Wasps have been hit by a number of injury problems in recent weeks and could now be without Bassett after he picked up the problem towards the end of last Saturday's 49-24 win over Gloucester.
The full extent of the damage has yet to be revealed but director of rugby Dai Young admits its does not look good.
"It looks quite a nasty injury, it's a high-end grade hamstring injury which, because of the Christmas period, is very hard to get a full report on," he said.
"I think it's due for a full report tomorrow but it looks like he'll be out for a while, that's for sure. He'd only been out for a couple of weeks and he's had a good season to date so it's disappointing.
"It seems to be the way our season's going at the minute. We get one player back, and you think you're going to get a little selection headache but it seems to sort itself out."