Burnett is dealing with a fractured right orbital bone suffered during a bunting drill. He had surgery on March 2 and was expected to miss two to three months but appears to be ahead of schedule. He is eligible to come off the DL on April 10 and manager Clint Hurdle said Wednesday that Burnett will start for the Class A Bradenton Marauders on Friday.
Morton is still recovering from offseason hip surgery. He is eligible to come off the DL on April 13.
The Pirates also placed reliever Chris Leroux on the 60-day DL with a strained right pectoral muscle suffered in an exhibition loss to Philadelphia on Tuesday.