De La Rosa, 25, was designated for assignment on Tuesday to make room on the 40-man roster for Cuban infielder Hector Olivera.
The Padres optioned De La Rosa to Triple-A El Paso.
De La Rosa was 2-0 with a 6.14 ERA in six appearances with Triple-A Oklahoma City, with six strikeouts and four walks in 7⅓ innings. The Dodgers claimed De La Rosa off waivers from the Athletics on April 30. On the season, De La Rosa is 2-0 with a 3.38 ERA in 13 games, with 10 strikeouts and nine walks in 13⅓ innings.
Left-handed batters are 2-for-13 (.154) against De La Rosa this season, with one home run and four walks.
De La Rosa pitched in 44 major league games in relief for the Diamondbacks in 2013-2014, putting up a 4.21 ERA with 48 strikeouts and 19 walks in 51⅓ innings.