Horwitz (hamstring) has begun a running program at the Pirates' spring training complex in Florida, Alex Stumpf of MLB.com reports.
Horwitz strained his left hamstring two weeks ago but has been cleared to kick off his running progression. If the first baseman is able to advance his rehab without any hiccups, he could begin a rehab assignment shortly after the All-Star break and return before the end of July.