Kirksey injured his hamstring in the second half of Sunday's loss against the Kansas City Chiefs.
The 26-year-old Kirksey registered 43 tackles and two interceptions in seven appearances this season. A team captain, the 6-foot-2, 235-pound Kirksey missed time earlier in the campaign with shoulder and ankle injuries.
Kirksey recorded 138 tackles, 3.5 sacks, two forced fumbles and one fumble recovery in 16 games last season.
Gaines suffered his second concussion in less than a month on Sunday on a first-quarter touchdown by Chiefs running back Kareem Hunt. He had just returned from missing the previous two games with a concussion that he sustained in practice.
The 26-year-old Gaines also missed the season-opening tie against the Pittsburgh Steelers with a knee injury.
Gaines, who signed with the Browns in March, collected 13 tackles and an interception in six games.
The fifth-year veteran was a sixth-round pick of the then-St. Louis Rams in 2014 and missed the entire 2015 season with a Lisfranc injury. While with the Rams, he played under current Browns interim head coach Gregg Williams.
Gaines, who is listed at 5-foot-10 and 191 pounds, was traded to Buffalo as part of the Sammy Watkins deal last year and made 11 starts for the Bills. He had 59 tackles, an interception and three forced fumbles in those games.
Filling one of the roster spots is defensive back Juston Burris, who was signed off the New York Jets' practice squad.
The Browns also signed defensive back Arrion Springs to the practice squad and released offensive lineman Jake Eldrenkamp.