Morrow, who hasn't pitched in a game since July 2018, had the arthroscopic procedure last November.
"He certainly worked really hard in an attempt to come back and tried a lot of different techniques and procedures, and just wasn't able to get over the hump," Epstein said Wednesday before the Cubs played the San Francisco Giants.
The Cubs signed Morrow to a two-year, $21 million deal in December 2017. He had 22 saves and a 1.47 ERA in 35 appearances in the first half of the 2018 season before the elbow issue flared up.
The team holds a $12 million option for 2020 (with a $3 million buyout), so it's unlikely the 35-year-old will return next season even if healthy.