  The recent gamma-ray burst GRB 130427A has an isotropic electromagnetic
energy $E^{iso}\sim10^{54}$ erg, suggesting an ample supply of target photons
for photo-hadronic interactions, which at its low redshift of $z\sim0.34$ would
appear to make it a promising candidate for neutrino detection. However, the
IceCube collaboration has reported a null result based on a search during the
prompt emission phase. We show that this neutrino non-detection can provide
valuable information about this GRB's key physical parameters such as the
emission radius $R_{d}$, the bulk Lorentz factor $\Gamma$ and the energy
fraction converted into cosmic rays $\epsilon_{p}$. The results are discussed
both in a model-independent way and in the specific scenarios of an internal
shock model (IS), a baryonic photospheric model (BPH) and magnetic photospheric
model (MPH). We find that the constraints are most stringent for the magnetic
photospheric model considered, but the constraints on the internal shock and
the baryonic photosphere models are fairly modest.
