Curtis was recalled from Double-A on Wednesday.
Curtis will rejoin the Diamondbacks, who placed Andrew Chafin on the 15-day DL and optioned Zack Godley to Triple-A in corresponding moves. The former sixth-round pick owns a 2.57 ERA at the Double-A level but struggled in 14 relief appearances with the Diamondbacks earlier this season, posting a 5.23 ERA.