The Spain international did not travel with the rest of the squad that departed for Amsterdam, with Jack Rodwell (hamstring), Javi Garcia (thigh) and Maicon (foot) also missing out.
Silva sustained the injury on international duty and did not play in the dramatic 2-1 victory over West Brom at the weekend.
Though coach Brian Kidd said after the win at the Hawthorns that Silva had a chance of featuring against Ajax, he has instead been given permission to return to Spain for further treatment.
Silva is also a big doubt for City's home game against Swansea next weekend.
City have just one point from two games in the Champions League so far this season and need to beat Ajax in their back-to-back meetings to have a realistic chance of reaching the knockout stages.