The Welshman had to be replaced with just over 20 minutes remaining of yesterday's Scottish Cup semi-final win over Aberdeen because of a hamstring injury and is now in doubt for the Easter Sunday showdown at Ibrox.
Ledley says he will certainly not play against Kilmarnock on Wednesday night in a bid to get fit for 'Gers.
"I am not sure about it at the moment. I will have a scan and we will see what that says, but I don't think I will be involved at Kilmarnock on Wednesday," he said.
"I played a pass and it sort of tightened up a bit.
"I tried to see if I could run it off, but there was no point in risking it at this stage of the season. I just hope it's stiff or a minor strain.
"This is the big part of the season and I feel I am hitting great form right now, so that's why I really hope it is nothing too big.
"I hope I can be fit for Sunday, but we will just have to wait and see what the scan says.
"I will probably go into training first and put some ice on it before going for the scan.
"It has been a while since I got injured and I am disappointed, but the team played well and made the final, that is the main thing.
"If I have to miss out for a couple of weeks I am sure that someone else will come in and do just as well."