Experimental measurements of magnetic fields generated in the cavity of a self-injecting laser-wakefield accelerator are presented. Faraday rotation is used to determine the existence of multimegagauss fields, constrained to a transverse dimension comparable to the plasma wavelength similar to lambda(p) and several lambda(p) longitudinally. The fields are generated rapidly and move with the driving laser. In our experiment, the appearance of the magnetic fields is correlated with the production of relativistic electrons, indicating that they are inherently tied to the growth and wave breaking of the nonlinear plasma wave. This evolution is confirmed by numerical simulations, showing that these measurements provide insight into the wakefield evolution with high spatial and temporal resolution.