The January signing from PSV, who has scored two goals in seven games in all competitions for Spurs, completed the full 90 minutes in the 1-1 draw at Turf Moor.
But head coach Jose Mourinho had earlier bemoaned the workload for his players, who exited the FA Cup last week but are still in the Champions League.
Bergwijn has been forced to play through the middle, along with Dele Alli and Lucas Moura, in the absence of injured attacking stars Harry Kane and Son Heung-min.
England captain Kane posted a video update of his return to training on Monday, but he is not expected back in the first team until May.
No estimated return date was given for Bergwijn, meanwhile, with a Tottenham statement adding: "The Netherlands international will now undergo an extended period of rehabilitation where his progress will continue to be assessed."
The 22-year-old will be a big miss for Spurs in their Champions League last-16 second leg at RB Leipzig.
Mourinho's men are 1-0 down following the home leg as they visit the Bundesliga side on Tuesday.