The England forward, one of six props in Sir Clive Woodward's 44-man Lions squad to tour New Zealand, will not play for his club again this season.
Stevens suffered a knee injury during Bath's Premiership victory over London Irish, which has now been diagnosed as a grade one posterior cruciate-ligament strain.
The verdict was delivered by London-based knee specialist Andy Williams, although Bath believe Stevens could be close to full fitness when the Lions tackle Argentina in a pre-tour game at Cardiff's Millennium Stadium on May 23.
"On consultation with the knee specialist, I can confirm that Matt has sustained a very strong grade one strain to his posterior cruciate ligament," said Bath's head of physical preparation, Chris Mallac.
"He should be back running in three weeks and will hopefully be close to full fitness for the Lions game against Argentina.
"If not, he will be fully fit shortly afterwards."
Stevens, 22, has won five England caps, and can pack down on either side of the scrum, giving Woodward and his coaching staff a valuable front-row option.
But injuries are threatening to affect Woodward's selection plans, with Stevens and his England colleague Graham Rowntree (knee) both suffering knocks since the Lions squad was announced earlier this month.
Gloucester tighthead Phil Vickery, meanwhile, is unlikely to recover from a broken arm in time.
Woodward, however, has left the door open, match fitness permitting, for Vickery, Jonny Wilkinson and Mike Tindall to fill additional squad places.