The Premier League club had initially said the 64-year-old, favourite to take over as England manager from Fabio Capello next July, would be set to return to work in two weeks following Wednesday's operation.
"[The doctor's] telling me I shouldn't even think about [returning] for at least four to five weeks. I hope to be back before then," Redknapp told Sky Sports News.
Redknapp said he would try to stay calm in front of the television while watching Spurs visit Fulham in the Premier League later on Sunday.
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