Silva sustained a thigh injury while on international duty with Spain, and has returned to Manchester.
The 27-year-old is now a doubt for City's match against Stoke in the Premier League on Saturday.
A statement from the Spanish Football Federation read: "After the issues reported by the player David Jimenez Silva after this afternoon's training session, a scan took place and a light muscle injury was detected.
"For precaution, and to avoid complications with this injury, Silva left the training camp.
"National coach Vicente del Bosque has decided not to call up anyone else to cover the absence."