The 32-year-old midfielder has played just one league game this campaign due to a toe injury, and recent attempts to return to training have proved unsuccessful.
Mowbray believes that Arca may have made his last appearance for the club.
"I don't think Julio is going to make the rest of the season," he told Sky Sports News. "I had a chat with him today and he's had a setback with his toe. He had trained for the last three or four days and looked really good in training.
"Julio is a quality footballer with the ball at is feet and he had pepped training up. But after this setback I'm not anticipating seeing him again this season.
"It's a shame for him and for the club. We wish him well and if we don't see him again it will be a disappointing end because he's out of contact in the summer."
Arca has made 200 appearances for Boro since joining them from Sunderland in 2006.