"My feeling is Andy will at least miss a start, just because," Cashman told ESPNNewYork.com's Ian O'Connor prior to receiving the test results.
After going just five innings in his start Wednesday and feeling stiffness in his arm, Pettitte underwent an MRI that determined the injury.
"Anytime you are talking about the area around the elbow, you start to worry a little bit," Pettitte said through a team spokesman.
Pettitte (4-0) first felt the stiffness in his previous start against the White Sox. The Yankees limited his throwing between starts to try to alleviate the problem but were unsuccessful.
Manager Joe Girardi could not pinpoint exactly where the stiffness occurred, but he said it has moved around on Pettitte's arm.
As Pettitte threw his 77 pitches during the Yankees' 7-5 victory over the Orioles, Girardi and pitching coach Dave Eiland asked him after every inning to give them updates on the arm.
Finally, they coaxed him into admitting he had the stiffness in the fifth.
"We weren't going to push it," Eiland said.
Pettitte, 37, has put a lot of miles on his left arm. In his career, Pettitte has pitched 2,965 1/3 innings, which is second most to Tim Wakefield among active pitchers.
On top of this, though, Pettitte has thrown what amounts to more than an extra season in the playoffs. His 249 postseason innings have worn on his elbow.
In his career, Pettitte's been on the disabled list five times because of elbow injuries. He also went on the DL in 2004 because of a strained left forearm. In 2008, he had back spasms.
Girardi said Pettitte's age and wear is a factor.
"He is not 25," Girardi said. "There are a lot of innings."
The Yankees are already dealing with the ineffectiveness of Javier Vazquez, whom they are skipping on Friday in Boston and instead are having him start on Monday in Detroit.
Andrew Marchand covers baseball for ESPNNewYork.com. Follow him on Twitter.