An investigation has been launched into the incident, which occurred late on Saturday.
ADVERTISEMENTGreek police say that a female migrant has been killed by gunfire while trying to cross the border from Turkey.
The woman died as a group of migrants attempted to cross the Evros River on Saturday night, police said in a statement.
Officers were patrolling the area near the river -- also known as the Meric -- when they reportedly spotted numerous migrants on the Turkish side.
Greek police said eleven people were found on board an inflatable dinghy, and officers directed flashlights at the boat and ordered them to "go back".
In response, a "barrage" of shots allegedly erupted from the Turkish side, while Greek officers fell to the ground and fired warning shots.
It was not immediately clear who fired the shot that killed the female migrant, and a Greek autopsy showed that the victim was shot in the back with a small-calibre weapon.
An investigation has been opened into the incident.
Four migrants were able to reach the Greek shore while a fifth body was recovered from the water, Greek police said.
The group had allegedly paid €2,000 each to smugglers in Istanbul to take them to Athens, according to the statement.
A large number of migrants have tried to cross the Evros River -- which narrows to about 60 to 70 metres -- to enter the European Union.
In February, nineteen migrants were found frozen to death at the Greece-Turkey border near İpsala.