Wilson (back) was activated from the 60-day injured list and designated for assignment by the Rays on Thursday, per the MLB.com transaction log.
Caminero went 1-for-3 with a solo home run in Wednesday's 4-0 win over Colorado.
Warren (8-5) took the loss against St. Louis on Wednesday, allowing three runs on seven hits and one walk while striking out five across 5.1 innings.
Martinez (11-3) earned the win Wednesday over the Rockies, allowing six hits over 5.2 scoreless innings. He struck out four.
Caballero is out of the lineup for Wednesday's game against the Cardinals.
Manager Aaron Boone said Wednesday that he expects Schmidt (elbow/forearm) to play catch Thursday, Jorge Castillo of ESPN.com reports.
Williamson was removed from Wednesday's game against the Rockies due to a hamstring injury, Ryan Bass of Rays.tv reports.
Yankees manager Aaron Boone said Wednesday that Judge (rib) has been cleared to begin light activities, which includes outdoor running and upper-body resistance work, Erik Boland of Newsday reports.
Bednar notched a save against the Cardinals on Tuesday, intentionally walking one batter and striking out three over 1.1 scoreless and hitless innings.
Diaz is absent from the lineup for Wednesday's game against Colorado, Ryan Bass of Rays.tv reports.
