We report $^{31}$P NMR measurements under various magnetic fields up to 7 T for the intermediate valence compound EuNi$_2$P$_2$, which shows heavy electronic states at low temperatures. In the high-temperature region above 40 K, the Knight shift followed the Curie--Weiss law reflecting localized $4f$ states. In addition, the behavior corresponding to the temperature variation of the average valence of Eu was observed in the nuclear spin-lattice relaxation rate $1/T_1$. With the occurrence of the Kondo effect, $1/T_1$ was clearly reduced below 40 K, and the Knight shift becomes almost constant at low temperatures. From these results, the formation of heavy quasiparticles by the hybridization of Eu $4f$ electrons and conduction electrons was clarified from microscopic viewpoints. Furthermore, a characteristic spin fluctuation was observed at low temperatures, which would be associated with valence fluctuations caused by the intermediate valence state of EuNi$_2$P$_2$.
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