The Marlins placed Rojas on the 60-day disabled list on May 9, and in a best-case scenario could return around the All-Star break.
"The good news is no damage on the ligaments or any of that," Rojas said. "We're looking forward to a speedy recovery. The doctor is going to give me the green light to start swinging with one hand, taking ground balls. For the bone to heal, it's going to be four to six weeks."
Manager Don Mattingly estimates a more conservative return date for Rojas, who was seeing more regular play at shortstop before he fractured his thumb while swinging the bat against the Mets on May 7.
The Marlins also are without shortstop Adeiny Hechavarria, who was placed on the 10-day disabled list Wednesday with a left oblique strain.
It's the second time this year Hechavarria has been on the DL with an oblique issue. However, the symptoms aren't exactly the same.
"I didn't hear a grade on it, but listening to Adeiny, it was worse than last time, and some of the symptoms, it's a little bit of a different area, also," Mattingly said. "I think the first one was a little bit more of an abdominal strain. This one is more of a true oblique; it's out on the side. He had trouble, coughing."
Hechavarria is expected to miss at least two or three more weeks.
As for the pitching staff, Wei-Yin Chen (left arm fatigue) and Jeff Locke (left shoulder tendinitis) remain on the 10-day DL.
Chen is dealing with an elbow issue, and he will be further evaluated by team doctors Monday.
Locke, who has been out since Spring Training, is throwing in rehab assignment games at Class A Advanced Jupiter. He's already made two starts, and may pitch at Double-A Jacksonville and Triple-A New Orleans, before being reinstated.
Either way, Locke likely will make at least two more rehab starts before joining the Marlins.
"I know he's getting built up, pitch count-wise," Mattingly said. "I think they're trying to get him out of Jupiter.
"I would think two more [rehab starts], unless something emergency-wise here had to happen. His pitch count has been built up."
Joe Frisaro has covered the Marlins for MLB.com since 2002. Follow him on Twitter @JoeFrisaro and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.