The gun battle, which lasted for several minutes, took place in a forest close to the border with Chhattisgarh.
A police team led by District Superintendent of Police Akhileswar Singh, which included personnel from the district voluntary force, raided the site and retaliated when the extremists fired at them.
"Fourteen Maoists were killed. Arms were also seized," Inspector General of Police Soumendra Priyadarshi told IANS.
Malkangiri, over 600 km from state capital Bhubaneswar, is considered a stronghold of Maoists.
Spotted: Sridevi's daughter Jhanvi Kapoor in Bandra
Photos: Kajol, Sridevi, Raveena Tandon at Mumbai airport
Photos: Akshay Kumar, Anushka Sharma, Ranveer Singh at Umang 2017
Photos: Sunny Leone, Shah Rukh Khan on Salman Khan's 'Bigg Boss 10'
Birth anniversary special: Remembering Subhas Chandra Bose