Johnson was with the Colts last Sunday but did not play in their win over the Jacksonville Jaguars. Matt Hasselbeck started the game in place of injured Andrew Luck.
Johnson was waived Monday before rejoining the Colts two days later. Hasselbeck was ill on Tuesday and did not practice.
The 6-foot-3, 210-pound Johnson has played in 29 career NFL games and started five. He has completed 96 of 177 passes for 1,042 yards with five touchdowns and 10 interceptions for the San Francisco 49ers (2014), Cincinnati Bengals (2013), Cleveland Browns (2012) and Tampa Bay Buccaneers (2008-2011).
Brown, who signed with the Colts as a free agent last November, suffered a groin injury during Sunday's game against the Jaguars. He played in their first four games this season and started three. He had 15 tackles and one pass defensed.
In 43 career NFL games with the Colts and Kansas City Chiefs, Brown has 40 tackles (37 solo), four passes defensed, one forced fumble, one fumble recovery and 17 special teams tackles.