Townsend, 24, was an unused substitute in Monday's win over Aston Villa and was pictured pushing and arguing with Gardiner on the pitch after the game.
"He did not train with the group. He is not available to be selected," Spurs boss Mauricio Pochettino said.
"It's because of Monday. If you behave the wrong way you always need to pay."
Townsend has yet to start in the Premier League this term and Pochettino preferred to bring on Ryan Mason and 18-year-old Josh Onomah in the second half against Villa.
"It's always my decision when he is available again to be part of the squad.
"Discipline for me is very important. I can understand the player - we have a young squad and a player can make a mistake - but when you cross the limit it is important to stop that.
"Has he apologised? Yes, he recognised it was a mistake," Pochettino added.
"I can understand because I was a player and when you don't play you're unhappy and sometimes your expectation is bigger than the manager provides you.
"But it was not normal behaviour. He is young and you need to understand that it isn't the way to impress the manager."
Pochettino stressed that Townsend, who progressed through the Spurs academy and made his first-team debut in 2011, does still have a future at White Hart Lane.
"All players have a future. It's up to them to have a future here. Football can change quick," he said.
"He is in the squad because we believe in him and believe he can give us very good things, but it is up to the player when he has the chance to impress me and show I am wrong in my decision."
Tottenham's Andros Townsend has been left out of Thursday's Europa League tie with Anderlecht after clashing with Spurs fitness coach Nathan Gardiner.