The three rockets caused no initial damage when they hit an empty area in the centre of the Turkish town, which has been repeatedly struck by rockets fired from Syria over the last months.
However the policeman was killed and two soldiers wounded when they went to destroy the unexploded ordnance, which blew up, the Kilis governor's office said in a statement.
The Turkish army meanwhile said it responded to the rocket attack with artillery fire according to the rules of engagement.
The necessity of ending cross border rocket strikes like the latest attacks on Kilis was one of the reasons given by the government for the operation.
Kilis has come under repeated attack from rocket fire from Syria in the last months, with 23 people killed, over half of them Syrian refugees.