Planck says not.

*One Planck time is the time it would take a photon traveling at the speed of light in a vacuum to cross a distance equal to one Planck length. Theoretically, this is the smallest time measurement that will ever be possible, roughly 10*^{−43} seconds. Within the framework of the laws of physics as we understand them today, for times less than one Planck time apart, we can neither measure nor detect any change. As of May 2010, the smallest time interval uncertainty in direct measurements is on the order of 12 attoseconds (1.2 × 10^{−17} seconds), about 3.7 × 10^{26} Planck times.source - https://www.quora.com/What-is-the-significance-of-Plancks-time

Although it is theoretically the smallest measurable time, it is no proof time itself is quantized...