The 64-year-old was admitted to hospital on Tuesday night for tests and will have an operation on a minor blockage in one of his arteries.
Redknapp is unable to travel with the Tottenham squad to Russia for their Europa League fixture against Rubin Kazan on Thursday.
Spurs are in top spot in Group A, two points ahead of Greek side PAOK.
Assistant manager Kevin Bond and first-team coach Joe Jordan will assume first-team duties in Redknapp's absence.
It is not known how long Redknapp will be away from work, though an update is expected later on Wednesday at the club's news conference in Russia.
Redknapp told the Sun on Wednesday he was confident the problem would not stop him taking charge of Sunday's Premier League match at Fulham.
He said: "I'm hoping I can be back at work again in a couple of days."