The midfielder was replaced at half-time of the Firhill clash after suffering a dead leg just before the break.
And he now faces a couple of weeks out of action as he waits for the knock to heal.
The Thistle skipper has been in terrific form for Alan Archibald's side so far this season, with his loss a huge blow to the Jags boss as his side look to continue their flying start to the campaign.
Archibald said: "Sean will be out for longer than we thought.
"He has got a blood disorder so he struggles to recover from certain injuries.
"He went to hospital as a precaution just to make sure that he is OK. He will miss a couple of weeks I think. He got a dead leg on Friday.
"He has got a blood problem that means he can take longer to recover. He had a similar thing last year when he picked up a calf problem.
"It is a blow for us because he has been outstanding for us. You could see the difference when he went off on Friday night.
"We didn't dominate the second half like we did the first after Welshy went off and that is no coincidence.
"We have got a break coming up. We have got a couple of games then it is the international break, so it has maybe come at a good time."
Welsh is not the only Jags star who is currently out of action, with defender Jordan McMillan no closer to a first-team return from the ankle injury he picked up in the pre-season draw with Cypriot side AEL Limassol.
The former Rangers and Dunfermline star has yet to play a competitive fixture for the SPFL Premiership newcomers this season - and boss Archibald admits the right-back's knock is causing consternation at Firhill.
He said: "Jordan's injury is not healing up. It is a nightmare for him and for us.
"It is a shame for him because he did most of the pre-season and then he got an injury in the Limassol game.
"I think we are going to send him for a scan to be on the safe side because it hasn't cleared.
"He took a knock on his ankle and we thought it would be a couple of weeks but it has not got any better. We are disappointed that it has taken longer than we first thought."
Having seen two points slip through their grasp on Friday night as the Jambos nicked a late draw at Firhill, Thistle are gearing up for a trip to Motherwell this weekend as they look to make it four games unbeaten in the top flight.
The Jags have failed to find the net in both of their home games so far this season but hit three times in their terrific win over Ross County ten days ago. Former Celtic and Hearts striker Craig Beattie trained with Thistle last week, but Archibald is not desperate to bolster his attacking arsenal.
He said: "We scored three goals at County. The week before everyone was saying we needed a striker then we scored and we didn't need one.
"We have got good strikers here. I am confident Dools (Kris Doolan) and Bairdy (John Baird)can score goals for us. My only concern is if they get injured.
"I would like to get one in but just to give us a bit of extra competition and back-up.
"It is not easy. Everyone is looking for the same type of goalscorer and they are not cheap."