Grandal was hitting .312 with five homers and 14 RBIs when he was injured.
"Grandal hit [earlier in the week] in the batting cage and off the tee and soft toss," manager Bud Black said. "He did fine, so he hit Tuesday in San Diego and took two days off. Hit again today, we suspect he will hit again tomorrow, possibly on the field, and then we'll just keep moving forward, but he's doing well."
Grandal will likely go on a rehab assignment before being activated.