The encounter took place when a BSF team was searching the Tumkimarka forest in Gamphakunda gram panchayat, Kalimela Inspector in-Charge, S K Nayak said.
The BSF man was injured in the hand.
The Maoists, some of whom were believed to be injured, fled after the encounter, he said.
The search was launched following the kidnap of three persons, including the son of a Sarpanch and a woman, from Gamphakunda village by Maoists last night.
One of those kidnapped managed to escape.