The officer and three others were on duty along the Evros River when shots came from the Turkish side shortly after 6 p.m. on Saturday.
The injured man was rushed to hospital in the nearby town of Didymoteicho where he underwent surgery, Greek police said.
They added that the guard, who had been hit by a bullet fired from a pistol, was in stable condition.
A police statement said: “The incident is being investigated by the relevant Greek authorities.”
According to reports in Greek media, police believe the gunman or men were most likely human traffickers.
Greece has been a gateway to Europe for migrants and refugees from the Middle East, Africa and Asia since 2015.