Salah started the match on the bench but came on in the second half to help lift the home side, who had been struggling to break down the resilient Danish team.
Diogo Jota opened the scoring in the 55th minute after tapping in Trent Alexander-Arnold’s pass then five minutes later Reds boss Jurgen Klopp made a double switch, bringing on Salah and Sadio Mane.
Salah sealed all three points in the final minute when he scored from the penalty spot after being brought down by Paulinho.
There appeared to be minimal contact between Salah and Paulinho but after the final whistle, BT Sport captured the Egyptian hobbling through the tunnel and into the dressing room.
Klopp did not mention Salah’s problem post-match but he will be desperate for it not to be serious after losing Fabinho to injury in the first half.
The Brazilian, who is filling in at centre-back with Virgil van Dijk already out, went down with a muscle injury in the 29th minute and had to be replaced by Rhys Williams.
It has been a hectic season so far – so make sure you don’t miss a single thing by signing up for the brilliant new Mirror Football newsletter!
All the latest transfer news and big stories will land straight into your inbox. You won’t miss out.
To sign up, put your email at the top of this article or follow the instructions on this link.
Klopp said: “Fab, I don’t know. Muscle injuries are like this, you get the result tomorrow morning probably, we have to wait for that.”
Liverpool could be boosted by the return of Joel Matip with Klopp adding: “I don’t know, we have to see.
“Look, if it would be only one game we play, if it was the last game of the season, I think we could make probably one or the other fit for one game – but we play three days later again and we need players again.
“The players who are now injured, we cannot use them on the first day of being fit again – or not injured anymore. They need a proper build-up for the rest of the season and that’s what we try.
“It is this juggle all the time between the fit players – how much can they play still? – and when we can use the others again?
“We are really interested in that fact so you can imagine we try everything to make everybody fit as quickly as possible.”