The 29-year-old centre-back turned his left ankle during the second half of last Saturday's 4-0 win over West Brom.
"When your mind is positive it's easier to recover," said the Argentine boss. "He doesn't require surgery.
"We have players that can perform in his place and we are very happy with the squad and the players we have."
Analysis: The best defence? the most powerful midfield? - How good are Tottenham?
Vertonghen has played in 20 out of 21 league matches this season, forming part of a defence that has conceded just 14 goals - the best record in the league.
Pochettino, however, was unsure as to when attacking midfielder Erik Lamela would return to action. The 24-year-old has been sidelined since the end of October with a hip problem.
"He will have a scan on Friday," he added.
"Still it is difficult to give the time that he can come back. We need to wait tomorrow because there is still some problems, and we are still not sure of the diagnosis."
Tottenham defender Jan Vertonghen is expected to be out for six weeks with an ankle ligament injury, according to his manager Mauricio Pochettino.