"I'm sure he'll get surgery within the next couple of weeks and have to go on IR," Shanahan told reporters after Friday's practice.
Shanahan was asked how the injury occurred.
"No one fell on it," he responded. "Two people, him and an O-lineman pushing on each other, and came to a stop, and [the knee] just gave out. It was a real unfortunate one."
Shanahan said the team plans to promote defensive lineman Kevin Givens from the practice squad to take Taylor's roster spot.
"Kevin had a good training camp, was close to making our roster," Shanahan said. "He sat here and worked all year to get better, and he's been waiting for this opportunity, and he got it yesterday."
Givens has "a chance to be" active on Sunday against the Seahawks, Shanahan added.
Taylor, 24, was working his way back from a ligament injury in his elbow and was inactive for the 49ers' last three games.
The loss of Taylor is another hit to the defensive line's once-strong depth. The unit has already lost Ronald Blair, D.J. Jones, and Damontre Moore for the season. Pass rusher Dee Ford, whom the team traded for in March, has missed four of the last five games and isn't expected to be available until the playoffs.
The 49ers made Taylor a seventh-round selection out of Temple last year. He registered nine combined tackles and a pass defensed through six games this season and has recorded 16 combined tackles and a pass defensed through his two NFL seasons.
San Francisco signed Givens, 22, in April as an undrafted free agent out of Penn State. He registered 33 combined tackles, 10.5 for a loss, five sacks, and a pass defensed as a junior in 2018.
The 49ers waived Givens on August 31 and then signed him to the practice squad the next day.