Wilson (1-2) allowed two earned runs on three hits and a walk while striking out one across 0.2 innings to blow the save and take the loss Tuesday against the Twins.
Manager Bob Melvin said Monday that Wilson (hip) has resumed playing catch at the Padres' facility in Arizona, but the right-hander has yet to start throwing off a mound, MLB.com reports.
The Padres placed Wilson on the 15-day injured list Wednesday with left hip inflammation.
Wilson (1-2) took the loss and was tagged with a blown save Sunday against Milwaukee, giving up four runs on one hit and three walks over one-third of an inning.
Wilson (pectoral) was activated from the 15-day injured list Friday, Dennis Lin of The Athletic reports.
Wilson (pectoral) tossed a simulated inning Saturday, per MLB.com.
Wilson was placed on the 15-day injured list with a right pectoral strain Tuesday.
Wilson earned a hold against Tampa Bay on Saturday, striking out two batters in one inning.
Wilson worked the eighth inning during Sunday's loss to Milwaukee, tossing a scoreless frame during which he allowed one walk and no hits.
Wilson will start Thursday's game against the Dodgers, Dennis Lin of The Athletic reports.