Aims. We studied the properties and occurrence of narrowband whistler waves and their interaction with strahl electrons observed between 0.17 and 0.26 au during the first encounter of Parker Solar Probe. Methods. We used Digital Fields Board band-pass filtered (BPF) data from FIELDS to detect the signatures of whistler waves. Additionally parameters derived from the particle distribution functions measured by the Solar Wind Electrons Alphas and Protons (SWEAP) instrument suite were used to investigate the plasma properties, and FIELDS suite measurements were used to investigate the electromagnetic (EM) fields properties corresponding to the observed whistler signatures. Results. We observe that the occurrence of whistler waves is low, nearly ~1.5% and less than 0.5% in the analyzed peak and average BPF data, respectively. Whistlers occur highly intermittently and 80% of the whistlers appear continuously for less than 3 s. The spacecraft frequencies of the analyzed waves are less than 0.2 electron cyclotron frequency (fce). The occurrence rate of whistler waves was found to be anticorrelated with the solar wind bulk velocity. The study of the duration of the whistler intervals revealed an anticorrelation between the duration and the solar wind velocity, as well as between the duration and the normalized amplitude of magnetic field variations. The pitch-angle widths (PAWs) of the field-aligned electron population referred to as the strahl are broader by at least 12 degrees during the presence of large amplitude narrowband whistler waves. This observation points toward an EM wave electron interaction, resulting in pitch-angle scattering. PAWs of strahl electrons corresponding to the short duration whistlers are higher compared to the long duration whistlers, indicating short duration whistlers scatter the strahl electrons better than the long duration ones. Parallel cuts through the strahl electron velocity distribution function (VDF) observed during the whistler intervals appear to depart from the Maxwellian shape typically found in the near-Sun strahl VDFs. The relative decrease in the parallel electron temperature and the increase in PAW for the electrons in the strahl energy range suggests that the interaction with whistler waves results in a transfer of electron momentum from the parallel to the perpendicular direction.