The Argentinian midfielder is now unlikely to feature before the end of the season when his contract at the Riverside Stadium expires.
Arca is Boro's longest-serving player and has made 185 appearances since joining from Sunderland in 2006, scoring nine goals.
But only three of those appearances, with one in the league, have come this season due to surgery to correct the 32-year-old's troublesome toe complaint.
"I don't think Julio is going to make the rest of the season," said manager Tony Mowbray. "I had a chat with him 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 his 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 contract in the summer."