Upon stimulation, plants elicit electrical signals that can travel within a cellular network analogous to the animal nervous system. It is well-known that in the human brain, voltage changes in certain regions result from concerted electrical activity which, in the form of action potentials (APs), travels within nerve-cell arrays. Electro- and magnetophysiological techniques like electroencephalography, magnetoencephalography, and magnetic resonance imaging are used to record this activity and to diagnose disorders. Here we demonstrate that APs in a multicellular plant system produce measurable magnetic fields. Using atomic optically pumped magnetometers, biomagnetism associated with electrical activity in the carnivorous Venus flytrap, Dionaea muscipula, was recorded. Action potentials were induced by heat stimulation and detected both electrically and magnetically. Furthermore, the thermal properties of ion channels underlying the AP were studied. Beyond proof of principle, our findings pave the way to understanding the molecular basis of biomagnetism in living plants. In the future, magnetometry may be used to study long-distance electrical signaling in a variety of plant species, and to develop noninvasive diagnostics of plant stress and disease.