Ripkowski, 26, did not play last season after the Packers waived him at the start of the season. The Packers made him a sixth-round choice in 2015, and he spent three seasons in Green Bay.
He signed a futures contract with the Chiefs in January.
Mondeaux, 23, and Crockett, 24, have never played a regular-season game.
The Chiefs signed defensive end Tim Ward on Friday. Ward, an undrafted free agent, played at Old Dominion, where he made 31 tackles for loss and 14.5 sacks in his four-year career.