The club also placed right-handed reliever Dale Thayer on the 15-day disabled list, retroactive to June 17, with a strained right shoulder.
To make room for Mateo on the 40-man roster, the Padres moved right-handed pitcher Brandon Morrow (right shoulder inflammation) from the 15-day DL to the 60-day DL. The righty, whose DL stint is retroactive to May 3, could begin a Minor League rehabilitation stint in the next week. He would then be eligible to rejoin the Padres on July 3.
Quackenbush has a 3.10 ERA in 20 1/3 innings this season with the Padres. This is the second time he's been promoted from El Paso. He was optioned there on June 10.
Mateo, 31, had a 1.86 ERA with nine saves with El Paso. He had 39 strikeouts in 29 innings and allowed 17 hits.
Mateo, who signed a Minor League free-agent deal with the Padres in January, last appeared in the Major Leagues on July 4, 2011, as a member of the Cubs. He had a 5.04 ERA in 44 2/3 innings with the Cubs from 2010-11.
The Padres were impressed with Mateo's work last year in the Dominican Winter League, where he was named MVP and Pitcher of the Year after posting a 1.75 ERA and a league-best 21 saves.
Then-Padres senior vice president Omar Minaya saw him last winter, as did some of the team's Dominican scouting staff. In January, Minaya left the Padres to become a special adviser to Major League Players Association head Tony Clark.
"I went into the offseason and winter ball trying to get better," Mateo said through an interpreter. "The numbers that I put up in the Dominican put a lot of attention on his name. The Padres came to me and offered a job. I went up there and took it. I just wanted to prove that I'm a good pitcher and deserved another chance."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.