Zabaleta suffered the injury in the victory over Portsmouth at the weekend after an accidental blow from Kevin-Prince Boateng but he is keen to maintain his record of playing every game under new manager Roberto Mancini.
Vincent Kompany has been ruled against Hull with a groin strain while Patrick Vieira remains doubtful with a calf injury.
Meanwhile City have been criticised by Real Madrid's sporting director Jorge Valdano after being linked with midfielder Fernando Gago in the transfer window.
City apparently moved in for Gago after their attempt to bring McDonald Mariga from Parma broke down and he joined Inter Milan instead.
Speaking to El Pais, Valdano said: "They had nothing prepared, not even one document signed.
"They had not reached an agreement with the player and they would have needed to do everything in 40 minutes."
Gago's agent Marcello Lombilla told radio station Onda Cero: "City used us. This has never happened to me before.
"I don't want to talk about the figures that City were offering because they approached Madrid without even knowing there wasn't physically enough time to put something together."
Source: PA
Source: PA