The England international took a heavy blow to his right knee during Bath's 21-19 Zurich Premiership victory over London Irish at the Madejski Stadium.
Stevens limped off the field after 17 minutes and could face a race against time to be fit before Sir Clive Woodward's squad leaves for New Zealand on June 24.
His injury came as another blow to Lions coach Woodward after Leicester pair Graham Rowntree and Lewis Moody were substituted during the Tigers' European Cup semi-final defeat by Toulouse.
A Bath spokesman said: "There is possible concern to Matt's right posterior cruciate ligament and he will be seeing a London specialist early next week.
"Through our physiotherapist's experience of this type of injury, he believes it could take four to six weeks to recover."
Bath head coach John Connolly added: "I know that the general prognosis of these injuries are that they're generally not operable and will take a bit of time to recover from.
"We don't think he will be available for us again this season but I also don't want to comment on whether he will be fit for the Lions."
Bath, however, have at least lifted themselves up to third in the Premiership - above Sale Sharks and within reach of a play-off place - thanks to the win, although they were indebted to Chris Malone.
The fly-half kept his side in the running and then slotted a crucial injury-time drop goal to steal victory.
The Exiles, desperate to win to ease any relegation fears, had looked like they had done enough with a Michael Horak try, four Barry Everitt penalties and a conversion.
But that was not to be the case and they are now left having to sweat it out with fellow relegation candidates, Worcester, Northampton, Leeds and Northampton, despite scoring a bonus point.