We propose a dissipative phase transition in a head-to-tail Bose Josephson junction. The quantum phase transition has the same origin as the one in a resistively shunted Josephson junction, but the intrinsic momentum coupling between the Josephson mode and the bath modes enables us to observe the dissipative phase transition without any synthetic dissipation. We show that the interatomic interaction strength plays the role of the damping parameter. Consequently, in contrast to a resistively shunted Josephson circuit, the Bose Josephson junction can exhibit an insulating phase in a wider parameter region by increasing the repulsive interaction strength, which is robust against nonperturbative effects. We argue that tight transverse confinement of the quasi-one-dimensional atomic gas allows us to reach the insulating phase.