Howe added that Burkhead will "get an MRI to confirm" the suspected injury.
Burkhead, 30, was carted off the field early in the third quarter. He had four carries for seven yards and two catches for five yards in the loss.
The veteran running back has been a key part of the team's revolving platoon at running back, with Damien Harris currently headlining the unit. In his past four games, Harris has rushed 63 times for 337 yards and two touchdowns.
The Patriots will also have Sony Michel going forward after he was activated from injured reserve this week, though he didn't play Sunday.
Burkhead was having an excellent year, rushing for 274 yards, catching 25 passes for 192 yards and recording six total touchdowns. He was on pace to set career highs in all of those statistical categories before Sunday's injury.
It's another tough blow for a Patriots team that finds itself at just 4-6 on the season and in danger of missing the postseason for just the second time since 2002. A division title is also all but out of the question, as the team trails the Buffalo Bills (7-3) and the Miami Dolphins (6-3) in the AFC East.
This isn't the season the Patriots and their fans would have wanted in the first year of the post-Tom Brady era. Potentially losing Burkhead for the year will make the team's uphill climb to get back into the postseason picture all the steeper.