Liam Kitching stepped in for the Polish international, with Barnsley's backline protecting their lead well after Carlton Morris put them in front early on, only for the hosts to buckle in the final quarter with Reading securing a point thanks to Josh Laurent's leveller eight minutes from time.
The result maintained the fourth-from-bottom Royals' five-point advantage over the Reds, who occupy the final relegation position.
Asbaghi said: "Mich, unfortunately for us, got injured in training after coming back from international duty.
"Of course, it is a tough injury for us and he has been one of our best players recently.
"I don't know, we will assess him and will get the right answers. But at least until Monday, we have to wait and I think we will have a good picture on Monday in terms of how long he will be out.
"In the worst case, maybe he is not here and he is not playing any more this season. The best case is that he can still play some games."
On his side's point - the third time in the past four home matches that the Reds have failed to hold onto a 1-0 lead and found themselves punished late on, he added: "It was two teams fighting to survive and there was a lot of tough fighting and with the pitch also.
"It was about winning a lot of second balls and after we got the lead, I thought we defended the lead in a good way.
"For me to be really happy, we needed to create more chances. But Reading are a team with a lot of offensive quality and that is their strength, with players like Swift, Joao, Ince and Drinkwater.
"When these players are desperate at 1-0 down, they take a lot of risk. They have to defend.
"We defended really well, they did not create one chance until they scored the goal. That was tough on us."
On whether the Reds paid the price for dropping too deep, he continued: "For the first 65 to 70 minutes, we were pressing them really high. After minute 65, we got a little bit more tired.
"When you try to press high and they take the risks that they did, it is pretty normal for a team - especially in our situation - not to go pressing high all the time.
"We have seven games left. None are mission impossible to win. We still have the confidence in the team, even if this feels a little bit like a loss."