The cycle-bomb, more familiar in Assam, exploded with a deafening sound at a super market complex at busy Chowpathy in the central part of the town, the Jalpaiguri SP, Ananth Kumar, said.
The bomb was a powerful one, though its exact nature was being ascertained, IG, north Bengal, K L Tamta said.
Asked if it could be the handiwork of the ULFA, he said, "Why should ULFA insurgents come here? Two years ago there was a similar cycle-bomb explosion at Barobisa in the Alipurduar sub-division."
Tamta said the whole area had been cordoned off and the injured had been admitted to a Alipurduar sub-divisional hospital.
One of the two persons killed has been identified as Sujit Das, 27, Tamta said.
Extremists of Kamtapur Liberation Organisation and ULFA are active in the area.