Rajsthali police OC Wahidullah Sarkar said on Wednesday that Su was arrested from an under-construction mosque at Islampur around 3am.
The operation to nab Renin Su was jointly conducted by BGB's Major Shabbir Ahmed, Major Kamal Pasha and OC Wahidullah Sarkar.
Renin Su is now in police custody at the Rajsthali Police Station.
The separatist leader is a medical graduate who has lived in Netherlands.
For the last few years, he has been living in Rangamati since he married a local Marma tribal girl.
He has a house in Rajsthali, police said.
Bangladesh security agencies say Renin Su has since then been a commander of the separatist Arakan Army.
On Aug 24, guerillas of the Arakan Army attacked a joint patrol of the Bangladesh Army and the Border Guard Bangladesh (BGB) at Thanchi in Bandarban district.
After that, the security forces have been trying to track down Renin Su.
They raided his Rajsthali house two days after the Thanchi attack. Renin Su could not be found but his lieutenant Ong U Rakhine was nabbed from there.
Cloth for combat fatigues used by the Arakan Army were seized along with cameras, laptops, propaganda material and two horses.
Ong U Rakhine admitted last month before a Rangamati court that he was a member of the Arakan Army.
He also provided information about Renin Su.
Two caretakers of the Rajsthali house—Mong Chu Aung Marma and Chui Aung Marma—are now in police custody.
Bangladesh police has shut down the bank account of an Arakan Army leader Renin Su and his close relatives.