Mujica was designated for assignment Sunday.
Mujica recorded a hold in Thursday's win over the Orioles. He pitched two innings, allowing an earned run on two hits while striking out two.
The Tigers will promote Mujica on Thursday, Chris Cotillo of SB Nation reports.
Mujica was reassigned to minor league camp on Sunday, Evan Woodbery of MLive.com reports.
Mujica faces long odds to make the Detroit bullpen out of spring training, The Detroit News reports.
Mujica signed a minor league deal with the Tigers that includes an invite to spring training, Tommy Stokke of FanRag Sports reports.
Mujica was released by the Royals on Thursday, Jeffrey Flanagan of MLB.com reports.
Mujica signed a minor league deal with Kansas City on Friday.
Mujica was granted his release from the Phillies on Thursday, Stephen Gross of The Morning Call reports.
Mujica has a 3.86 ERA, 21 saves and a 25:3 K:BB in 35 innings for Triple-A Lehigh Valley this season.