Matsui (3-2) took the loss against the Angels on Tuesday, allowing three runs on one hit and two walks without retiring a batter.
Matsui earned a hold against Atlanta on Friday, walking one batter and striking out two over two-thirds of an inning.
Matsui struck out two batters and allowed one hit in a scoreless inning against Oakland in San Diego's Cactus League finale Wednesday.
Padres manager Mike Shildt told 97.3 The Fan that "there is a possibility" Matsui (back) will be ready for San Diego's opening regular-season series in South Korea.
Matsui (back) will throw a bullpen session Tuesday, AJ Cassavell of MLB.com reports.
Matsui (back) resumed playing catch Friday, Jeff Sanders of The San Diego Union-Tribune reports.
Matsui underwent an MRI on his back which showed inflammation but no structural damage, Dennis Lin of The Athletic reports.
Manager Mike Shildt told reporters Sunday that Matsui is dealing with back spasms and will not pitch against the Cubs, Dennis Lin of The Athletic reports.
Matsui signed a five-year, $28 million contract with the Padres on Saturday, Jeff Passan of ESPN.com reports.
Matsui has exercised his international free agent rights and will pursue a major-league contract this winter, Yakyu Cosmopolitan reports.