As supporters jumped up and down in unison in front of the players at full time, the stand gave way – although reports say no-one was injured.
Hubert Bruls, the mayor of Nijmegen, called for an investigation and said he was “very shocked by what happened”.
Nikolai Baden Frederiksen scored the winner in the first half.
Bruls told Dutch newspaper De Telegraaf: “Fortunately, as far as is known, no-one was injured. I want an investigation into what happened here as soon as possible.”
“It was shocking,” Vitesse defender Riechedly Bazoer told Dutch broadcaster NOS. “Fortunately, everyone survived.”
“A stadium which should be safe is collapsing. This must be investigated,” the Netherlands” KNVB football federation said.
A spokesperson for the government agency responsible for investigating such incidents said it had not yet been decided whether an investigation would be opened.
Vitesse move up to sixth in the table and host Premier League side Tottenham in the Europa Conference League on Thursday.