In his Physics commentary, Thomas Wylton reports and rejects an opinion about time that posits the existence of minimal times conceived of as indivisible parts of time. This opinion is in contrast with the view that time is continuous, the predominant view in the late Middle Ages. In this paper I first explain the notion of minimal time. I then focus on the relation between the existence of minimal times and the existence of minima naturalia in the extension of natural bodies. In particular, I present the two ways in which the author of the opinion in question deduces the existence of minimal times from the existence of minima naturalia in the extension of natural bodies. I also briefly present the reaction of Wylton against this opinion. I finally explain how in this opinion the position of minimal times is relevant to the problem of the existence of time. The Appendix to the paper contains Wylton's report of the opinion about minimal times.