"Appreciate the support and all that have reached out the past couple of days. Look forward to attacking the process and coming back better than ever in 2021," he wrote on Instagram.
Burkhead was carted to the locker room early in the third quarter of Sunday's 27-20 loss after taking a direct hit on his right knee on a third-down run in which he was stopped short and remained down for an extended period of time.
The injury left the Patriots with just two running backs -- Damien Harris and James White -- for the remainder of the game. Sony Michel was activated off injured reserve Saturday but was inactive for Sunday's game. Undrafted rookie J.J. Taylor was also inactive.
Entering Sunday, Burkhead had 63 rushes for 267 yards and three touchdowns to go with 23 receptions for 187 yards and three touchdowns.
ESPN's Mike Reiss contributed to this report.