The Scot, who has played 27 times for the club this season, will now miss both legs of the Champions League quarter-final against Real Madrid - the first of which is in the Spanish capital on Tuesday.
The news comes as a bitter blow to Tottenham boss Harry Redknapp, who is already without a number of defenders.
Knee injury: Alan Hutton will be out for around a month
Ledley King, Jonathan Woodgate and Younes Kaboul are all injured while William Gallas is a serious doubt for tomorrow's match at Wigan and Tuesday's game in the Bernabeu because of a knee problem.
Michael Dawson and Sebastien Bassong are Redknapp's only two fit natural centre-halves, while Hutton's rival at right-back, Vedran Corluka, can also play there if needed.
The Spurs boss will now be hoping that none of Corluka, Bassong or Dawson is injured in tomorrow's game at the DW Stadium.
Should Spurs overcome the odds and beat Real Madrid, Hutton would likely miss the first leg of the Champions League semi-final but should be available for the return fixture.
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Explore more:People: Michael Dawson, William Gallas, Jonathan Woodgate, Harry Redknapp, Younes Kaboul, Alan Hutton, Sebastien Bassong, Ledley King Places: Madrid