No-one was injured in the incident, which reports said was believed to be in protest against a forthcoming visit to Turkey by Pope Benedict XVI.
The Pope, due to arrive on 28 November, angered Muslims in September by quoting a medieval text which said the Prophet Muhammad had brought "evil" things.
He has since expressed his regrets for offending Muslims.
"We think that this is something that is an isolated incident and does not disturb the overall calm preparations for the trip," chief Vatican spokesman, Father Federico Lombardi, told Reuters news agency.
The protester threw his gun into the garden of the consulate after firing the shots, the Dogan news agency said.
The man shouted, "I am happy to be a Muslim," the agency reported.
Pope Benedict XVI will visit Ankara, Izmir, Istanbul and ancient Ephesus during his trip to Turkey, which will be his first visit to a predominantly Muslim country.
The Pope was officially invited to visit the country by the Turkish government and will be there until 1 December.
