Tuilagi suffered the injury during his first Premiership game of the season against Newcastle at the weekend - a game Leicester Tigers won 31-6.
And Tigers director of rugby Richard Cockerill believes the injury is likely to rule Tuilagi out of England's Test matches this autumn.
"Manu has a suspected torn pec muscle in his chest," he said.
"He's going for further investigation and it is hard to tell how long he will be out, but it's going to be weeks leading to months potentially.
"These things happen. Hopefully, he will not be out for too long. Six to eight weeks at best but it may be longer depending how much damage there is."