  Fast radio bursts (FRBs) are radio bursts characterized by millisecond
durations, high Galactic latitude positions, and high dispersion measures. Very
recently, the cosmological origin of FRB 150418 has been confirmed by
\cite{kea16}, and FRBs are now strong competitors as cosmological probes. The
simple sharp feature of the FRB signal is ideal for them to probe some of the
fundamental laws of physics. Here we show that by analyzing the delay time
between different frequencies, the FRB data can place stringent upper limits on
the rest mass of the photon. For FRB 150418 at $z=0.492$, one can potentially
reach $m_{\gamma} \leq 5.2 \times 10^{-47}$ g, which is $10^{20}$ times smaller
than the rest mass of electron, and is about $10^3$ times smaller than that
obtained using other astrophysical sources with the same method.
