The German centre-half got the injury in stoppage-time at the Vitality Stadium as North End held on to their 3-2 lead - Bauer had scored their third goal.
He went down after stretching to make a challenge and stayed on the floor, clearly in distress as he shouted out in pain a number of times.
If it found that he has torn the tendon, the recovery is measured in months and surgery will be required.
North End manager Alex Neil said: "We are naturally devastated, disappointed and upset for Patrick Bauer, he's got a really bad injury and it looks like his Achilles.
"The squad, myself and everyone connected with Preston is upset about that. When he's available, Pat is an ever-present for us and is a big character.
"We want to get him a speedy recovery and look after him the best we can. I'm sure he will come through."
Neil spoke to Bauer in the dressing room before conducting his post-match media duties and not surprisingly reported that he was not in a good way.
"Patrick was inconsolable afterwards, gutted, because it is a lot of get your head round when you are a competitor and a footballer," said Neil.
"We will get him the best treatment we can.
"I didn't actually see what happened. He went down and the game continued.
"At first I thought it was his knee then I could see he was in distress, making signals to come off which is highly unusual for Patrick.
"I could see how upset he was and I realised then it was going to be something significant."
"We had the doctor with us so he will take the lead with that. I would imagine we could get him in for surgery as early as Wednesday.
"In my experience of players having that type of injury, it gets done quickly.
"Generally when players get this type of injury, they get the feeling that someone has kicked them from behind and actually no one is there.
"It is not good news, we have spoken about key injuries and that is another one."
Bauer's injury took the gloss of a great victory which was North End's fifth on their travels in Championship action this season.
Goals from Tom Barkhuizen, Scott Sinclair and Bauer had put them 3-0 up, before Junior Stanislas brought it back to 3-1 with 19 minutes left.
Then in the 86th minute, Sam Surridge headed Bournemouth's second to set up a tight finish.
Bauer's injury which came early in stoppage-time, meant 11 additional minutes were eventually played.
Neil said: "In terms of the actual game I thought we performed very well and were well worth the win.
"At 3-0, in terms of how we went about it, I thought we were quite comfortable.
"It took a quality free-kick to get them back in the game, we hadn't put a foot wrong until then. The foul was soft, it went into Surridge and he let out a scream and went down.
"Stanislas then produced a bit of quality.
"We regained control of the game without dominating the ball if that makes sense. We made passes and worked our way up the pitch.
"Then they wriggled away from us down the left hand side of the pitch and produced a cross to score again.
"At that sage I'd been reluctant to make any changes because when you are playing that type of team and are on top, it is all about getting distances right and narrowing those gaps.
"Sometimes when you bring substitutes on, they don't get those distances right for a couple of minutes and it can hurt you.
"As soon as they scored the second, I needed to make changes to freshen us up to see it out.
"We hung on and won the game."
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