Defoe could also be forced to sit out England forthcoming 2010 World Cup qualifiers against Ukraine and Belarus later this month.
"He is struggling," Spurs boss Harry Redknapp has said.
"Jermain dislocated two fingers against Burnley last Saturday and they couldn't get them back in.
"But he has also fractured his hand. He spent all Saturday night in hospital and is struggling.
"Hopefully, he'll be OK for England but we'll have to wait and see."