The 28-year-old female police officer sustained serious leg injuries when she was struck by a car in Eglinton Place and remains in hospital for treatment.
A 58–year-old man has been arrested in connection with attempted murder and enquiries are continuing.
A 59-year-old man has also been arrested and charged in connection with the incident and is due before Kilmarnock Sheriff Court on Friday, 25 June.
A report will be submitted to the Procurator Fiscal.
Detective Inspector Stephen McCulloch from Kilmarnock CID said: “I would like to thank members of the public for their positive response to this appeal and also reassure the local community that Police Scotland will continue to tackle violent crime, ensuring the area is a safe place for everyone.
“Anyone with information or concerns regarding crime in their community is urged to contact their local police station or 101.”