We experimentally study timing jitter of single-photon detection by NbN superconducting strips with width $w$ ranging from 190 nm to $3\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$. We find that timing jitter of both narrow (190 nm) and micron-wide strips is about 40 ps at currents where internal detection efficiency $\ensuremath{\eta}$ saturates and it is close to our instrumental jitter. We also calculate intrinsic timing jitter in wide strips using the modified time-dependent Ginzburg-Landau equation coupled with a two-temperature model. We find that with increasing width the intrinsic timing jitter increases and the effect is most considerable at currents where a rapid growth of $\ensuremath{\eta}$ changes to saturation. We relate it with complicated vortex and antivortex dynamics, which depends on a photon's absorption site across the strip and its width. The model also predicts that at current close to depairing current the intrinsic timing jitter of a wide strip could be about $\ensuremath{\hbar}/{k}_{B}{T}_{c}$ (${T}_{c}$ is a critical temperature of superconductor), i.e., the same as for a narrow strip.