Spurs drew 1-1 with Everton at Goodison Park on Sunday, but the match was overshadowed by the injury which left Son in tears.
Referee Martin Atkinson initially showed Son a yellow card before brandishing a red moments later, after seeing the severity of Gomes' injury.
Spurs manager Mauricio Pochettino was furious with the decision and said VAR failed to help the match officials.
"The VAR need to check if it was a bad tackle and not a bad injury," he told a news conference after the game. "It was clear that it was never the intention of Son to create the problem that happens after.
"It was unbelievable he received the red card. I never complain about the VAR, but please -- we need use it in the best way. It is going to change the spirit of football."
Everton said Gomes had a successful operation to repair a fracture dislocation to his right ankle on Monday, but he is expected to be sidelined until next season.
Son is set to miss the next three Premier League matches for Spurs against Sheffield United, West Ham United and Bournemouth.
The forward would be available to face Manchester United at Old Trafford in the Premier League on Dec. 4.
Meanwhile, Everton are investigating a supporter who allegedly racially abused Son during the match.
A statement from Everton Fan Services read: "Everton strongly condemns any form of racism. Any such behaviour has no place within our stadium, our club, our community or our game."