Number eight Dan Ward-Smith is already out of action for the next six months with knee ligament damage and Alfie To'oala sidelined by hamstring trouble.
As a result new signing Andrew Blowers, who arrives from New Zealand on Monday, will be drafted straight into the side to face Wasps next Sunday.
"Matt Salter dislocated the same shoulder against Harlequins earlier this season and he needs an operation on it now so that's him out for the season," said Bristol coach Richard Hill.
"It makes our back-row problems even worse with Ward-Smith and To'oala both out and the Blowers signing is looking a good decision now.
"Losing Matt is a big blow. He played great for us last week and with the other two injured he was a key ball-carrier for us. Now we'll be struggling to find big powerful runners to carry the ball."
After Leicester's surprise 10-9 defeat against Northampton, second-placed Bristol might have gone back to the top of the table with a win at the Stoop.
But they struggled to contain Quins - particularly at the set-pieces - and conceded a string of penalties with fly-half Adrian Jarvis kicking five of them to earn a fifth win in six league games for the Londoners.
Although Bristol's David Lemi scored a first-half interception try and Jason Strange kicked an early penalty, they were then penned in their own half for long spells and lost flanker Joe El Abd to the sin-bin after the break.
"I did say that this was always going to be a tough game and we let ourselves down with our work at the set-pieces," said Hill.
"We have to accept that we've had an off day and we know we haven't been playing well recently. This was an accident waiting to happen."