Context. Collisions of galaxy clusters generate shocks and turbulence in the intra-cluster medium (ICM). The presence of relativistic particles and magnetic fields is inferred through the detection of extended synchrotron radio sources such as haloes and relics and implies that merger shocks and turbulence are capable of (re-)accelerating particles to relativistic energies. However, the precise relationship between merger shocks, turbulence, and extended radio emission is still unclear. Studies of the most simple binary cluster mergers are important to help understand the particle acceleration in the ICM. Aims. Our main aim is to study the properties of the extended radio emission and particle acceleration mechanism(s) associated with the generation of relativistic particles in the ICM. Methods. We measure the low-frequency radio emission from the merging galaxy cluster Abell 2146 with LOFAR at 144 MHz. We characterize the spectral properties of the radio emission by combining these data with data from archival Giant Metrewave Radio Telescope (GMRT) at 238 MHz and 612 MHz and Very Large Array (VLA) at 1.5 GHz. Results. We observe extended radio emission at 144 MHz behind the NW and SE shocks. Across the NW extended source, the spectral index steepens from −1.06 ± 0.06 to −1.29 ± 0.09 in the direction of the cluster centre. This spectral behaviour suggests that a relic is associated with the NW upstream shock. The precise nature of the SE extended emission is unclear. It may be a radio halo bounded by a shock or a superposition of a relic and halo. At 144 MHz, we detect a faint emission that was not seen with high-frequency observations, implying a steep (α < −1.3) spectrum nature of the bridge emission. Conclusions. Our results imply that the extended radio emission in Abell 2146 is probably associated with shocks and turbulence during cluster merger. The relativistic electrons in the NW and SE may originate from fossil plasma and thermal electrons, respectively.