The flying full-back was struggling at the end of Friday's qualifier at home to Finland, when the visitors snatched a shock 1-1 draw, and he will drop out of the squad to return to Barcelona for further tests.
The loss of first-choice left-back Alba is a setback to coach Vicente del Bosque as his side prepare to go in search of a victory in Paris on Tuesday that would put them back to the top of Group I.
Spain's draw against Finland saw them drop down to second place, two points behind group leaders France, who were 3-1 victors at home to Georgia.
Alba's injury is also a worry for Barcelona as he joins fellow defenders Carles Puyol and Adriano Correia in the treatment room with the Champions League quarter-finals looming at the beginning of next month.
His participation looks to be in doubt with the La Liga leaders travelling to play Paris Saint-Germain in their last eight first leg on April 2.
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