The 32-year-old Argentine midfielder has played just one league game this season due to a toe injury, and recent attempts at a return to training have ended without success.
"I don't think Julio is going to make the rest of the season," said Mowbray.
"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 is currently Boro's longest serving member of the first-team having joined from local rivals Sunderland in 2006. He has made nearly 200 appearances for Boro in that period, scoring nine times.