Spurs manager Mauricio Pochettino said it looked "very bad" when he spoke to reporters after the match in which Vertonghen rolled his ankle chasing down the ball on the touchline.
On Tuesday, 29-year-old Vertonghen tweeted: "Gutted to be injured but will be back as soon as I can."
Tottenham have been playing a 3-5-2 formation with fellow Belgian Toby Alderweireld and Eric Dier alongside Vertonghen.
Pochettino played fullback Ben Davies on the left of a back three for the second half on Saturday and could keep him there or play Austria international Kevin Wimmer.
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The Argentine could also return to a back four with England international Dier alongside Alderweireld.
Second-placed Tottenham, who trail Chelsea by seven points, visit Manchester City on Saturday.
(Writing by Ken Ferris; Editing by Greg Stutchbury)
