Tottenham manager Harry Redknapp has admitted that King, 30, is "nowhere near" a return after a recurrence of the injury during training in January.
With Michael Dawson and Younes Kaboul also out, Jonathan Woodgate may start the game at Blackburn on Wednesday.
King, who also suffers from chronic knee problems, has made only four league appearances this season and his campaign may now be over as he prepares for surgery.
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The centre-half, who won the most recent of his 21 England caps against the United States in June 2010, has suffered an injury-interrupted career, but appeared in 20 of Tottenham's Premier League matches last season.
His latest lay-off intensifies Redknapp's problems in the centre of defence.
Dawson is serving a three-match ban after being sent off in Tottenham's 4-0 defeat by Fulham in the FA Cup fourth round and Kaboul is out for six weeks because he requires surgery on his injured knee.
William Gallas, who came on as a substitute in the wake of Dawson's dismissal on Sunday, is playing despite being hampered by a hip injury.
Cameroon international Sebastien Bassong is fit, while Bongani Khumalo, who is yet to play for the club since signing from South African side Supersport, and versatile full-back Vedran Corluka could be pressed into service alongside him.
Source: BBC Sport
Source: BBC Sport