He said the injury is not a torn labrum, as had been reported on Wednesday.
Arroyo told MASN that he is waiting for a comparison to his previous MRI, but "it's not looking real good."
Arroyo will not have surgery. "It's either rehab or retire," he told MASN.
The 39-year-old Arroyo, a 15-year veteran with a 145-131 record and a 4.19 ERA, averaged 207 innings per season from 2004 to 2013 before undergoing Tommy John surgery on his elbow in 2014.
A 2006 National League All-Star with the Cincinnati Reds, Arroyo signed a minor league deal with the Nationals in January. He became a free agent in November when the Los Angeles Dodgers, who acquired Arroyo from the Atlanta Braves as part of a three-team deal at the July 31 trade deadline, declined a $13 million club option and paid a $4.5 million buyout.
Arroyo was scheduled to pitch Wednesday's exhibition game but was scratched with shoulder soreness. Manager Dusty Baker said Arroyo had felt soreness in the shoulder since last starting on March 10.
"The last start he was masterful," manager Dusty Baker told reporters Wednesday. "That's what kind of shocked us a little bit, how he didn't respond. Because he appeared like he was in no pain. But you just don't know. Especially as you get older, you don't know how you're going to respond between starts. That was the last test he had to pass."