Melville, 27, made his season debut for the Twins on Monday but was designated for assignment two days later. He surrendered five runs on four hits over 3 1/3 innings against the White Sox.
The 6-foot-4 right-hander offers an intriguing starting option with upside for the Padres and could be a September callup if all goes well. Melville posted a 4-3 record and a 2.70 ERA in 11 games (10 starts) for Triple-A Rochester.
Padres manager Andy Green said he was impressed by Melville's stuff after watching film of him on Friday night. He has fanned 64 batters in 66 2/3 frames in the Minors this season.
"It was 94-96 [mph] with a slider, a curveball and a changeup. I really like the curveball," Green said. "I think there's a lot to like there, and it's another starting option that gets into our Minor League system."
Melville, a fourth-round pick by the Royals in the 2008 Draft, will join Triple-A El Paso's rotation.
After striking gold on Hand last year and adding another solid bullpen piece in Kirby Yates off waivers this season, the Padres figured Melville was worth a flier.
"We've had some success doing it, and they're guys we really like," Green said.
• The transferring of Diaz (right forearm strain) to the 60-day DL doesn't mean much since he has been out for longer than 60 days. The Padres are hopeful the right-hander will return to the club within the next week. Diaz will make his next and -- if all goes well -- final rehab start at El Paso. In two starts at Class A Advanced Lake Elsinore, he gave up three runs over 7 1/3 innings.
• All signs point to Jhoulys Chacin making his Monday start against the Giants, Green noted, though he wouldn't say for sure. The right-hander is feeling better after jamming his throwing hand on Wednesday.
Patrick Pinak is a reporter for MLB.com based in Miami.