We present simulations of the very high energy (VHE) gamma-ray light curve of the Crab pulsar as observed by the Cherenkov Telescope Array (CTA). The CTA pulse profile of the Crab pulsar is simulated with the specific goal of determining the accuracy of the position of the interpulse. We fit the pulse shape obtained by the MAGIC telescope with a three-Gaussian template and rescale it to account for the different CTA instrumental and observational configurations. Simulations are performed for different configurations of CTA and for the ASTRI mini-array. The northern CTA configuration will provide an improvement of a factor of ~3 in accuracy with an observing time comparable to that of MAGIC (73 hours). Unless the VHE spectrum above 1 TeV behaves differently from what we presently know, unreasonably long observing times are required for a significant detection of the pulsations of the Crab pulsar with the high-energy-range sub-arrays. We also found that an independent VHE timing analysis is feasible with Large Size Telescopes (LSTs). CTA will provide a significant improvement in determining the VHE pulse shape parameters necessary to constrain theoretical models of the gamma-ray emission of the Crab pulsar. One of such parameters is the shift in phase between peaks in the pulse profile at VHE and in other energy bands that, if detected, may point to different locations of the emission regions.