The Padres also transferred right-hander Jason Marquis from the 15-day to the 60-day disabled list Thursday.
Hundley, expecting the birth of his first child with wife Amy, is hitting .231 in 82 games this season with a career high-tying nine home runs and 29 RBIs.
The 29-year-old Robinson will be making his first trip to the majors. He was batting .298 with 12 RBIs in 29 games with Tucson following his acquisition in a June 20 trade with Baltimore.
Marquis underwent season-ending Tommy John surgery on July 30.