Both were booked for fouls on Kevin de Bruyne which led to their respective injuries in the 0-0 Premier League draw and forced them both off the pitch.
"It's very bad news. Dann is an anterior cruciate ligament and Puncheon a rupture in the posterior cruciate ligament," Hodgson told a news conference after Palace's 2-1 win over Southampton at St Mary's on Tuesday.
"They will both see a specialist and (are) likely (to) undergo surgery when the swelling goes. We won't see them play again this season and they may not be ready for the next. (The result against Man City) came at a high price as we lost two of our most senior players."
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(Reporting by Rik Sharma,; Editing by Neville Dalton)
