BOSTON - Minor-leaguer starter James Kaprielian, a major piece in the Sonny Gray deal with New York, is dealing with some shoulder soreness as he returns from Tommy John surgery.

Kaprielian will resume his rehab program once the soreness subsides, according to A’s general manager David Forst.

Setbacks are common when recovering from elbow ligament replacement surgery. Kaprielian had hoped to be throwing in games in June or July; fellow minor-league starter Daulton Jefferies, who had Tommy John surgery the same week as Kaprielian, will start throwing in extended spring training games next month.

Jefferies, the A’s second-round pick out of Cal in 2016, could be pitching with Class-A Stockton in July.

Manager Bob Melvin said that pitchers Paul Blackburn (forearm) and Liam Hendriks (hip) threw to hitters at Class-A Stockton and that outfielder Boog Powell (knee) has started to do baseball activity.

Susan Slusser is a San Francisco Chronicle staff writer. Email: sslusser@sfchronicle.com Twitter: @susanslusser