Brown was placed on the waived-injured list with an undisclosed injury.
The Colts' move comes one day after Indy waived eight other players, including two that were hurt.
Hamlin spent 2009 and part of 2010 with Dallas, then finished last season with Jacksonville. He was the Cowboys' fifth-round pick in 2009 and has three career tackles in 12 games.
Brown was signed by Indy during last season's injury rash and finished with 24 tackles in 10 games.
All teams must trim their rosters to 80 by Tuesday afternoon.