To make room on the 25-man roster for Francisco, Warner Madrigal was optioned to Triple-A Oklahoma City. He was called up on June 30 for his fourth stint in the Major Leagues this season.
Both Feliz and Mathis are available for Sunday's game against the Mariners.
"We wanted to bring up a couple of guys who were fresh," Rangers general manager Jon Daniels said. "The last few games has taken a toll on the bullpen."
Kinsler's move was retroactive to July 29. He was suffering from a strained left hamstring that hadn't improved over the last three days.
The Rangers were hoping to avoid placing Kinsler on the DL, but Daniels didn't want Kinsler to feel pressured to come back before being completely healed. He is eligible to return Aug. 13. Kinsler was hitting .157 in July.
Feliz made 13 starts for Triple-A Oklahoma City, posting a 3-5 record with a 3.86 ERA. He made his first relief appearance on June 25 and has gone 1-1 with a 2.16 ERA in 12 outings.
Opponents have hit .169 against Feliz with 20 strikeouts and three walks over 16 2/3 innings. Baseball America ranked Feliz as the Rangers' No. 1 prospect and the No. 10 prospect in baseball at the start of the season. He last pitched on Friday.
The Rangers have thought about calling Feliz up since the All-Star break.
"We think he has the ability to help us, but we're not expecting him to save the day," Daniels said. "He's worked on some things, and he deserves the opportunity."
Mathis was optioned to Triple-A prior to Wednesday's game. He was pulled from a Triple-A start on Saturday and instead pitched one perfect inning.
Grilli, who has inflammation over his flexor tendon in his right elbow, has gone 1-1 with a 1.53 ERA in 17 relief appearances since being acquired from the Rockies this season.
Daniel Paulling is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.