Context. Beta Pictoris is an A-type star that hosts a complex planetary system with two massive gas giants and a prominent debris disc. Variable absorption lines in its stellar spectrum have been interpreted as signatures of exocomets ─ comet-like bodies transiting the star. Stellar flybys can gravitationally perturb objects in the outer comet reservoir, altering their orbits and potentially injecting them into the inner system, thereby triggering exocomet showers. Aims. We assessed the contribution of stellar flybys to the observed exocomet activity by reconstructing the stellar encounter history of β Pictoris in the past and future. Methods. We used Gaia DR3 data, supplemented with radial velocities from complementary spectroscopic surveys, to compile a catalogue of stars currently within 80 pc of β Pictoris. Their orbits were integrated backwards and forwards in time in an axisymmetric Galactic potential (via the GALA package) to identify encounters within 2 pc of the system. Results. We identified 99 416 stars currently within 80 pc of β Pictoris with resolved kinematics. Among these, 49 stars (including the eight components of five binaries) encounter β Pictoris within 2 pc between ─1.5 Myr and +2 Myr. For four of the binaries, the centre-of-mass trajectories also pass within 2 pc. We estimated the sample to be more than 60% complete within 0.5 Myr of today. Conclusions. Despite β Pictoris being the eponym of its famous moving group, none of the identified encounters involved its moving group members; all are unrelated field stars. We found no encounter capable of shaping the observed disc structures, although stellar flybys may contribute to the long-term evolution of an Oort Cloud-like structure. Our catalogue constitutes the most complete reconstruction of the β Pictoris encounter history to date and provides a robust foundation for future dynamical simulations.