The warrant was issued late on Thursday, accusing Sukur of "membership in an armed terror organization."
Turkey has launched a massive crackdown on alleged supporters of the movement led by Fethullah Gulen, detaining some 35,000 people and dismissing tens of thousands of others from government jobs. Gulen has denied involvement.
Sukur, who reportedly left Turkey last year, was a Turkey international who played for Inter Milan and Galatasaray. He was elected to parliament in 2011 but resigned from the ruling party following the government's rift with Gulen.
