Morse is expected to play three games and then start a rehab assignment soon thereafter.
The team is hoping that Morse returns to action on June 8, when it plays the Red Sox. However, according to Johnson, there are people in the organization who hope that Morse can play in a Major League game before that.
"In Morse's mind, he is ready tomorrow, as soon as he is playing one game," Johnson said. "His throwing is what aggravated his arm. I'm not worried about his hitting. He is always thinking about hitting, and he has been hitting on the sly, probably throughout this whole thing. I'm more worried about him throwing, and that could aggravate it."