On the disabled list since April 30 with a strained right hamstring, Stanton tested his legs on Monday at the Marlins' Roger Dean Stadium complex in Jupiter, Fla.
"Stanton is running the bases in Jupiter, which is good news," manager Mike Redmond said.
For players recovering from hamstring injuries, running the bases is one of the final steps before seeing game action.
However, no firm date has been set for Stanton to appear in rehab-assignment games.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter