Gaines sustained the injury during Sunday's 27-24 win over the Denver Broncos. The 26-year-old joins wide receiver De'Anthony Thomas and running back Akeem Hunt as being placed on injured reserve this week by the Chiefs, who host the Tennessee Titans in Saturday's wild-card matchup (4:35 p.m. ET).
Gaines recorded 30 tackles and three pass deflections in 14 games this season. He spent all four of his seasons with the Chiefs since being selected by Kansas City in the third round of the 2014 draft.
Defensive tackle Stefan Charles was signed to fill Gaines' roster spot. The 29-year-old Charles has collected 60 tackles, five sacks and two forced fumbles in 49 career games with the Tennessee Titans, Buffalo Bills, Detroit Lions and Jacksonville Jaguars.