James Kaprielian, the starter acquired in the Sonny Gray deal with the Yankees last year, has started to play catch again after being sidelined with a shoulder problem.

Kaprielian started throwing again two days ago, The Chronicle has learned, and the team will proceed cautiously with him. He was throwing bullpen sessions while rehabbing from 2017 Tommy John surgery when he first began to feel shoulder discomfort in May.

Daulton Jefferies, the former Cal starter who had Tommy John surgery the same week Kaprielian did last year, is throwing 95 mph off the mound and next week, he will make his first start since surgery, working in an Arizona League game.

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