It is a devastating blow for Cahill, who was hoping to claim a place in England's World Cup squad.
The 24-year-old will sit out the match against Manchester City on Tuesday after being taken ill last week, which caused him to miss the 0-0 draw with Fulham.
Cahill's replacement Andy O'Brien looks certain retain to retain his place in the team, providing he shakes off a thigh problem, and partner Zat Knight at the back.
Coyle said: "You are always disappointed when you lose one of your best players. You want them available all the time.
"When they are not available you go with the ones you have and you look for them to do their best.
"The players wear that shirt with pride here and will give everything they can. I am sure this group will do all in their power to win points for Bolton."
Cahill is due to be released from hospital on Monday after being detained since Saturday.
Coyle explained: "Gary suffered a pain in his arm and it became severely swollen on the day of the Fulham game.
"There was no way he could play so we took him straight off to hospital. It turns out he had a blood clot in his arm, so he is going to be out for a number of months.
"The clot needed to be resolved and in doing that you need the medication. It follows you can't play.
"It is a severe blow for the boy but our main concern is his welfare. We have to make sure Gary is fit and well.
"As disappointed as we are, at 24, he has a marvellous career ahead of him. I believe he would have made the World Cup for the summer but we have to make sure first of all he recovers from this blood clot."
Coyle has promised that the level of care afforded to Cahill will be second to none.
"I don't think it is a sport-related injury, I think it is just one of those things that can happen to anyone at any given time," said the Bolton boss.
"Gary will be disappointed as he has so much to play for. He is one of the best players at the club and he had a big role to play, no doubt about that.
"He also had a chance of going to the World Cup - but that chance will come again. He is a terrific lad and someone we love working with. He has a great mindset.
"Gary will get the best care available to him. As much as we love football, we will focus on making sure he recovers well."