Assistant head coach Joe Vitt says Lofton has a high ankle sprain. Hawthorne has a torn meniscus and was scheduled for surgery Monday.
Vitt is not specifying which leg either player hurt. He says he is hopeful Lofton will return for the Redskins game and possibly before the preseason ends.
Lofton, one of the Saints' top free-agent acquisitions, is expected to start this season at middle linebacker.
Vitt says that while Lofton is out, Ramon Humber will take over at middle linebacker, relaying defensive coordinator Steve Spagnuolo's calls on the field.