Black had been suffering from "shoulder weakness" late in spring training. He has since been rehabbing with the Mets High-A affiliate in Port St. Lucie. His fastball has been clocked between 93 and 96 MPH in his rehab appearances.
Black, 26, was acquired in 2013 from the Pirates along with second baseman Dilson Herrera in exchanges for C John Buck and OF Marlon Byrd.
In 41 appearances last season he posted a 2.60 ERA with the Mets. Black is expected to play a vital part in the bullpen as a middle reliever.