"Following further scans and examination, Jermain Defoe will undergo surgery after suffering a stress fracture in his right foot," said Tottenham in a statement.
"Early detection has allowed the club to opt for the best long-term treatment."
Defoe will miss the Carling Cup final against Manchester United at Wembley on 1 March while the returning Keane will also be absent because he is cup-tied.
Spurs are 14th in the table, but just one point clear of the bottom three with 14 Premier League fixtures remaining.
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