Kirk Meyer of the New York Daily News passed along comments Kay made Monday during an appearance on ESPN New York Radio: "Shame on Clint Frazier for not getting healthy."
After Frazier advised the longtime play-by-play man to "steer clear of publicly calling me out for not when we haven't even had one [conversation] about my concussion this year" in a Twitter message, Kay responded.
"Clint, I would never question someone's injury. Never," he wrote. "In fact, I have gone out of my way to say how I felt for you this year and how badly I know how you want to play. It is beyond my comprehension that you would think I would minimize what you are going through."
Kay added: "The next time I make light of someone's injury will be the first time. I should have said how unfortunate you and [Jacoby] Ellsbury's injuries are. It came out in a clumsy way. If you took it the wrong way, I apologize and look forward to speaking with you personally."
Kay was speaking about the Yankees' lack of depth because of injuries and also referenced Ellsbury in the remarks, which he later described as facetious.
Frazier, who started the 2018 season on the disabled list because of a concussion, played 15 games across three stints with the Yankees between trips in the minor leagues before getting placed back on the DL early last month with post-concussion migraines.
"I feel better. Much better than I did the last two weeks," he said July 25, per DJ Eberle of the Times Leader. "I'm just hoping that it continues to go that direction—it's frustrating whenever it doesn't. To know I feel good right now is better because it eases my mind more."
The 23-year-old Georgia native has compiled a .238/.295/.429 slash line with four home runs in 54 appearances across two seasons with the Yankees.
The team has not provided a timetable for Frazier's return. Shane Robinson will continue to provide New York with outfield depth for the time being.