The 64-year-old had two stents inserted to unblock coronary arteries and was in "excellent spirits" the club said in a statement on their website.
"We are delighted the operation went so smoothly and successfully," said Tottenham chairman Daniel Levy.
"Knowing Harry he will want to rush back, but it's important that he only does so when he has recovered properly."
Former West Ham United, Portsmouth and Southampton boss Redknapp will miss Thursday's Europa League game against Rubin Kazan in Russia but plans to return to work soon.
"I am hoping I can be back at work again in a couple of days," he was quoted as saying by British media before the operation.
Tottenham's Dutch forward Rafael van der Vaart said the squad were shocked to hear the news.
"We were totally surprised and I was a little bit scared for him when I heard," Van der Vaart told Sky Sports. "I hope he's going to get better and that we can keep winning for him."
Assistant coaches Kevin Bond and Joe Jordan will be in charge of the first team in Redknapp's absence.
Spurs are top of Group A with seven points from three matches, two ahead of PAOK Salonika and three in front of Rubin.
They have also been in good form in the Premier League, climbing to fifth in the table after a seven-match unbeaten run.
