Time and space aren't well defined, but current models indeed put a discrete limit on both: Planck-Length and Planck-Time (~1.9×10^−43s and ~5.7×10^−35m respectively).

Below these limits, physical descriptions of the world lose meaning, i.e. shorter time spans or distances don't result in measurable changes and our models break down. That doesn't mean these limits are "real" in the sense that space and time are indeed quantised, but experiments and observations end at these limits.