The injury occurred during the second quarter of the 48-32 defeat.
"We're hoping for good news on it, but if not, I know he'll do his rehab and be ready sometime next year," Shanahan told reporters.
When he is ready next year is the worrisome part.
The fact that the injury occurred so late during the season is potentially devastating news for the offensive line. The recovery for such an injury is typically in the seven- to nine-month range. That would put a potential return for Tomlinson at about late July to late September, which would obviously impact his availability for at least part of the 2019 season.
"He's a huge part of what we do," Shanahan added.
Tomlinson was replaced in the game by former first-round pick Joshua Garnett.
The 49ers signed Tomlinson to a three-year extension on June 22, keeping him with the 49ers through the 2021 season. The new deal is worth up to $18 million.