Degenerate two-dimensional electron liquids are theoretically established to possess two vastly distinct collisional electron mean free paths, where even-parity deformations of the Fermi surface are hydrodynamic with a short collisional mean free path but odd-parity deformations remain near ballistic (known as the "tomographic" transport regime). Predicted signatures of this regime rely on the scaling of observables with temperature or device dimension, both of which are difficult to establish with certainty. Here, we consider magnetotransport in a minimal model of tomographic electrons and show that even a small magnetic field suppresses tomographic transport signatures and thus acts as a sensitive and unique probe of this regime. Fundamentally, the magnetic field breaks time-reversal invariance, which is a prerequisite for the odd-even parity effect in the collisional relaxation. We analyze in detail the scaling of the transverse conductivity, which has been linked to small-channel conductance of interaction-dominated electrons, and show that a tomographic scaling regime at intermediate wave numbers is quickly suppressed with magnetic field to a hydrodynamic or collisionless form. We confirm that the suppression occurs at relatively small magnetic fields when the cyclotron radius is comparable to the ballistic mean free path of the dominant odd-parity mode. This occurs at a much smaller magnetic field than the magnetic field strength required to suppress hydrodynamic electron transport, which suggests an experimental protocol to extract the odd-parity mean free path.