The incident occured around 2 am on Friday in the Rajarchhara area of the Upazila's Sadar Union, said Teknaf Police OC Pradip Kumar Das.
The deceased were identified as the 40-year-old Nur Mohammed and the 35-year-old Nurul Amin.
They were both on the home ministry's list of 'yaba and hundi businessmen', the police said.
A police team launched a raid in the hilly area of Rajarchhara after being informed that ‘drug smugglers’ were meeting there, added the OC.
"The smugglers opened fire when the police arrived. The police retaliated causing the yaba smugglers began to retreat. Two people were shot in the crossfire."
The two drug suspects were then to the Teknaf Upazila Health Complex, where doctors on duty declared them dead.
Police recovered 20,000 yaba tablets, eight guns and 20 rounds of bullets from the scene.
Five policemen were also injured in the gunfight, added OC Pradip.