Bailly went down with a knee injury after Ander Herrera's slide tackle on Mateo Kovacic sent the Chelsea midfielder crashing into the defender.
He was replaced by Marcos Rojo in the 71st minute. Up to the 67th minute when Bailly went down, the former Villarreal man was enjoying a fantastic game at the heart of United's defence, particularly silencing Gonzalo Higuain - in tandem with partner Victor Lindelof.
The Red Devils had taken the lead through Juan Mata in the 11th minute, but a David de Gea mistake saw Marcos Alonso equalise before half time.
The injury comes as a huge blow to Bailly and Cote d'Ivoire ahead of the Africa Cup of Nations billed to start on June 21.
This season, Bailly had been on and off the treatment table but recently, he regained stability and form.