A high-frequency test of Coulomb's law is described. The sensitivity of the experiment is given in terms of a finite photon rest mass using the Proca equations. The null result of our measurement expressed in the form of the photon rest mass squared is μ2=(1.04+/-1.2)×10-19 cm-2. Expressed as a deviation from Coulomb's law of the form 1r2+q, our experiment gives q=(2.7+/-3.1)×10-16. This result extends the validity of Coulomb's law by two orders of magnitude.