Maddison broke down late on in the 1-1 draw, with Frank confirming a knee injury afterwards.
He said, "We're pretty sure it was the same knee he injured before."
Spurs had an early lead through Brennan Johnson before Harvey Barnes struck an impressive equaliser for Newcastle.
The match also marked Heung-min Son's final game in a Spurs shirt. Substituted midway through the second-half, Son was given a guard of honour by his teammates, while coaching staff also gave him a standing ovation as he left the pitch.
Frank also said: "I think it's very likely Sonny's last game because it's (a transfer to LAFC) very close.
"I think sometimes in life and football things can be both beautiful and brutal. That's what we got today. It looks like with Madders a bad injury and then on the other side unbelieveable scenes for Son from his team-mates and the respect from the Newcastle players.
"First we had the walkaround and then the team-mates gathered around and he was emotional. In the changing room it was more of the same. I just said a few things but not much because it's about Sonny and then he said a few things. It was beautiful."
"I thought a good game between two competitive teams. We scored a great goal from competitive pressure from winning the ball high. Then we dropped a little bit back before second half getting back to what we wanted."