"You won't see him until after the All-Star break, in our minds," Cashman said on MLB Network Radio's "The Front Office" show.
The Yankees previously didn't set a timetable for the ace's return to the team. Severino was diagnosed with a right lat strain last month and placed on the injured list.
Severino, who hasn't made his debut this season, is in the fourth week out of six in which he isn't allowed to throw. The pitcher will begin a throwing program after the six-week period.
Severino was rehabbing from right rotator cuff inflammation when he underwent an MRI on April 10 to find out why he couldn't return quickly. The MRI revealed the Grade 2 lat strain, and he later said he thought the injury occurred at the same time as the rotator cuff ailment.
Severino said he felt the initial injury while warming up for a spring training contest March 5.
The two-time All-Star pitcher posted a 19-8 record with a 3.39 ERA in 32 starts last season. Severino signed a four-year, $40 million contract extension with the Yankees in February.