  We report $^{51}$V nuclear magnetic resonance (NMR) studies on single
crystals of the multiferroic material FeVO$_4$. The high-temperature Knight
shift shows Curie-Weiss behavior, $^{51}K = a/(T + \theta)$, with a large Weiss
constant $\theta \approx$ 116 K. However, the $^{51}$V spectrum shows no
ordering near these temperatures, splitting instead into two peaks below 65 K,
which suggests only short-ranged magnetic order on the NMR time scale. Two
magnetic transitions are identified from peaks in the spin-lattice relaxation
rate, $1/^{51}T_1$, at temperatures $T_{N1} \approx$ 19 K and $T_{N2} \approx$
13 K, which are lower than the estimates obtained from polycrystalline samples.
In the low-temperature incommensurate spiral state, the maximum ordered moment
is estimated as 1.95${\mu}_B$/Fe, or 1/3 of the local moment. Strong low-energy
spin fluctuations are also indicated by the unconventional power-law
temperature dependence $1/^{51}T_1 \propto T^2$. The large Weiss constant,
short-range magnetic correlations far above $T_{N1}$, small ordered moment,
significant low-energy spin fluctuations, and incommensurate ordered phases all
provide explicit evidence for strong magnetic frustration in FeVO$_4$.
