The right-hander pinched something in the back of his shoulder while taking swings in the batting cage at Nationals Park on April 8. He was scheduled to start the next day, but was placed on the 15-day disabled list, retroactive to April 4.
"It's definitely gotten better over the last couple of days," Turner said. "I've been able to do everything pain free the last three days."
The 22-year-old right-hander is on the disabled list for the first time in his career.
"It was kind of a freak thing," Turner said. "I took a swing. I just felt something. It's in the back of the shoulder."
An MRI confirmed a shoulder sprain.
"It feels like it's getting better," Turner said. "That's the biggest thing. It didn't look like it was anything too serious."
Turner threw with no discomfort from 60 feet on Tuesday, and he will throw off flat ground again on Wednesday. If he keeps progressing, he could be throwing off the mound by the weekend.
Before he is ready to return to the rotation, Turner will make at least one rehab assignment start.
Brad Hand made two starts in Turner's absence. The lefty struggled Monday night, giving up four runs in three innings in Monday's 9-2 loss to the Nationals.