The 40-year-old man sprinted into Greece at the northeastern Kastanies border crossing just before midnight Monday, police said. The man told the court he had been drinking earlier, and that he would like to travel to Sweden, where his children live.
Local residents said Turkish soldiers apparently fired in the air while pursuing him.
A local misdemeanour court gave the man a four-month prison sentence, suspended for three years. He was placed in custody pending deportation to Turkey.
The incident came amid tension between the Turkey and Greece. Greece has boosted border patrols on its land border with Turkey after two Greek military personnel were arrested March 1 on the Turkish side of the border.
Greece said the men accidentally strayed across the ill-defined border due to bad weather, but both remain in a Turkish prison on charges of entering a military zone.