But it is undoubtedly a setback for the Premier League leaders as the England international has been one of their most impressive performers this season.
Cole returned to action in last week's 2-2 Champions League draw with Atletico after almost a fortnight out with the injury.
He will be one of a number of established names absent from Fabio Capello's squad for the friendly in Doha.
Rio Ferdinand and Steven Gerrard are also missing through injury, as are Aaron Lennon and Carlton Cole.
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