The ability to perform noninvasive and non-contact measurements of electric signals produced by action potentials is essential in biomedicine. A key method to do this is to remotely sense signals by the magnetic field they induce. Existing methods for magnetic field sensing of mammalian tissue, used in techniques such as magnetoencephalography of the brain, require cryogenically cooled superconducting detectors. These have many disadvantages in terms of high cost, flexibility and limited portability as well as poor spatial and temporal resolution. In this work we demonstrate an alternative technique for detecting magnetic fields generated by the current from action potentials in living tissue using nitrogen vacancy centres in diamond. With 50 pT/Hz sensitivity, we show the first measurements of magnetic sensing from mammalian tissue with a diamond sensor using mouse muscle optogenetically activated with blue light. We show these proof of principle measurements can be performed in an ordinary, unshielded lab environment and that the signal can be easily recovered by digital signal processing techniques. Although as yet uncompetitive with probe electrophysiology in terms of sensitivity, we demonstrate the feasibility of sensing action potentials via magnetic field in mammals using a diamond quantum sensor, as a step towards microscopic imaging of electrical activity in a biological sample using nitrogen vacancy centres in diamond.