Dogan news agency video footage of the scene showed the bishop lying dead in front of a building.
Mehmet Celalettin Lekesiz, the governor for the province of Hatay, said police immediately caught the suspected killer. He said the man, identified only as Murat A., was Padovese's driver for the last four and a half years and was mentally unstable.
"The initial investigation shows that the incident is not politically motivated," Lekesiz said. "We have learned that the suspect had psychological problems and was receiving treatment."
Padovese, who is the equivalent of the bishop for the Anatolia region, was scheduled to leave for Cyprus on Friday to meet with the pope, who is visiting the island, and fellow bishops from around the region to prepare for a synod of Roman Catholic bishops in the Middle East. The synod is scheduled for October.
The Vatican-affiliated Asia News agency cited unnamed witnesses as saying the driver appeared to be "depressed, violent and threatening," in recent days.
No one answered phones at his church in Iskenderun.
The Vatican spokesman, the Rev. Federico Lombardi, told The Associated Press in Rome that the Vatican felt "immense pain, consternation, (and) bewilderment" over the death and noted that it showed the "difficult conditions" of the Catholic community in the region.
He said the pope's upcoming visit to Cyprus and the upcoming synod of bishops on the Middle East showed "how the universal church is in solidarity with this community."
The killing is the latest in a string of attacks in recent years on Christians in Turkey, where Christians make up less than 1 percent of the 70 million population.
In 2007, a Roman Catholic priest in the western city of Izmir, Adriano Franchini, was stabbed and slightly wounded in the stomach by a 19-year-old man after Sunday Mass. The man was arrested.
The same year, a group of men entered a Bible-publishing house in the central Anatolian city of Malatya and killed three Christians, including a German national. The five alleged killers are now standing trial for murder.
The killings -- in which the victims were tied up and had their throats slit -- drew international condemnation and added to Western concerns about whether Turkey can protect its religious minorities.
In 2006, amid widespread anger in Islamic countries over the publication in European newspapers of caricatures of Islam's Prophet Muhammad, a 16-year-old boy shot dead a Catholic priest, Father Andrea Santoro, as he prayed in his church in the Black Sea city of Trabzon. The boy was convicted of murder and sentenced to 18 years in prison.
Padovese was appointed to his post in 2004.
Mustafa Sinanoglu, the mufti or top Muslim cleric for Hatay province, told the Anatolia news agency that he and Padovese had been working together toward establishing closer dialogue between their faiths.
"I have been deeply affected by the death of a colleague with whom I had been working together on projects for the region, Turkey and world peace," he said.
"These kinds of incidents are damaging our country's image," he added.
Asia News said the Bishop was also involved in work for the unity of the Christian church and to revive the tiny Christian community in Turkey.
Turkey's Culture Minister Ertugrul Gunay paid tribute to Padovese saying he had "made important contributions to the culture of tolerance through his services in Hatay."
The Foreign Ministry said the death of Padovese was an "important loss from a religious and scholarly point of view," adding that the Bishop had written extensively on Turkey.
In a 2006 telephone interview with the AP, following another knife attack that injured another priest, Padovese expressed concern over the safety of Catholics priests in Turkey.
"The climate has changed," he said. "It is the Catholic priests that are being targeted."