Both Hoyer and Buffalo quarterback EJ Manuel suffered serious injuries during the meeting of their teams on Thursday, a game won by Cleveland 37-24.
Hoyer and Manuel were both injured after they scrambled out of the pocket.
Cleveland Coach Rob Chudzinski said Hoyer, a former third-string quarterback who made his third straight start on Thursday, would require surgery.
Manuel is expected to be out of action for from four to six weeks with a sprained knee ligament.
Hoyer will be replaced by Brandon Weeden, who began the year as Cleveland's starter before suffering a thumb injury.
Jeff Tuel came in to replace Manuel and struggled against the Browns, eventually throwing an interception late in the contest that was returned for a game-clinching touchdown.
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