The Israeli company's technology helps people tag photos on the Web by figuring out who is in the pictures.
Face.com announced the purchase on its blog on Monday. Financial terms were not disclosed.
Face.com did not say whether its website will continue to run after the acquisition. Facebook commonly shutters sites that it acquires and folds in their employees to its work force. So far, Instagram, which it's buying for nearly $1 billion, has been the only exception.
Facebook confirms the deal but will not say how much it paid or what its plans are for Face.com.
Shares of the Menlo Park, Calif., company are up $1.51, or 5 percent, to $31.52 in afternoon trading Monday.
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