Defoe sidelined for six weeks
"It's his ankle. He had a scan last night and has an appointment with the specialist this afternoon. He will be out for six weeks or so because it's a bad one," Redknapp told reporters.
Defoe, who picked up the injury in England's 3-1 Euro 2012 qualifying victory over Switzerland on Tuesday, scored a hat-trick for his country in last Friday's 4-0 demolition of Bulgaria at Wembley.
The 27-year-old, who postponed groin surgery last month, is the second Spurs player to be injured on England duty after defender Michael Dawson was ruled out for eight weeks with a knee injury suffered against Bulgaria.
Spurs, who begin their Champions League group stage campaign away to German side Werder Bremen on Tuesday, travel to West Bromwich Albion in the Premier League on Saturday.