"You won't see him until after the All-Star break, in our minds," Cashman said on SiriusXM's MLB Network Radio's "The Front Office" show.
The Yankees hadn't issued a timeline for Severino's return, but it seemed likely that it would occur close to the All-Star break in July. Severino is resting from the right lat strain he was diagnosed with last month.
Severino is in the middle of the fourth week of six during which he isn't allowed to throw. He will resume a throwing program thereafter.
On April 10, while continuing rehab on a separate injury (right rotator cuff inflammation), Severino underwent an MRI to figure out why he hadn't been able to get back from the rotator cuff issue as quickly as anticipated. The lat strain was found on that MRI. Severino later said he believed the injury happened at the same time as the rotator cuff injury, which he felt while warming up for a spring training game March 5.
Along with the timeline on Severino, Cashman breezed through a few other injury updates Sunday:
Outfielder Clint Frazier, sidelined the past two weeks with a right ankle sprain, will rejoin the Yankees on Monday or Tuesday. Later Sunday, manager Aaron Boone announced that Frazier will be activated on Monday.
Frazier was to play in a rehab game Sunday with Double-A Trenton, but inclement weather forced the postponement of that game.
Starting pitcher James Paxton, placed on the IL on Saturday due to left knee inflammation, is looking at a "three-week-at-max" situation, according to Cashman. The left-hander received a cortisone shot this weekend and won't be doing any throwing for four to six days.
"He's gone through this before, where he has to take a timeout and get an injection and then get going again," Cashman said, referencing an injury he said Paxton had while in Seattle a few seasons ago.
Another pitcher, reliever Dellin Betances, will resume a throwing program on Monday. He recently received a cortisone shot as he continued his comeback from a right shoulder impingement. The injury has had him on the IL since spring training.
Cashman said it will be "sometime in June" that Betances is back in pinstripes.
"He's still a ways away," the GM said.
Giancarlo Stanton, on the IL since April 1, will be wrapping up his rehab from biceps and shoulder injuries this week, Cashman said. Manager Aaron Boone said the power-hitting outfielder/designated hitter did tee and soft-toss drill work Saturday and Sunday, and by Monday or Tuesday, he'll start ramping up to the point that he takes batting practice on the field.
By next weekend, the Yankees could start getting Stanton into rehab games.
Aaron Hicks, who signed a seven-year, $70 million contract extension near the start of spring training, has been shelved with lower back tightness since the beginning of March. At the time, the Yankees believed he would be down for only a couple of days. That turned into a longer-term injury that included a pair of cortisone shots as part of the recovery process.
The center fielder is participating in extended spring training games at the Yankees' facility in Tampa, Florida. As early as this week, Hicks could begin a rehab assignment with the High-A Tampa Tarpons, Cashman said.
"We're hopeful as early as next weekend he could get activated," Cashman said.
Shortstop Didi Gregorius, who had offseason Tommy John surgery, has progressed more quickly than expected. He could be looking at his own set of extended spring training games as early as the next two weeks. Later this week, he'll complete his rehab throwing program.
With his team at 18-14 entering play Sunday, Cashman said he is pleased with the way the Yankees have weathered their early-season injury storm.
"The record, where we stand despite that kind of adversity on the injured list, we'll certainly take and sign up for every day of the week," he said.