"Roman records directly attest such measuring of recruits, although determining the exact height requirement is problematic. Vegetius gives the minimum standard, or incomma, as “6 [Roman] feet [178 cm.] or 5 feet 10 inches [ca. 173 cm.] among the auxiliary cavalry or the [soldiers] of the legionary first cohort.”15 Although both Fritz Wille and N.P. Milner see Vegetius’s figures as an optimum and a minimum figure respectively, the expression incommam . . . exactam strongly suggests a regulation height.16 Vegetius may mean that cavalrymen must be 6 feet and soldiers of the first cohort five foot ten. In any case, these are clearly height requirements for elite sol- diers and not for the entire military. Praetorian Guardsmen probably had a higher minimum height than rank and file legionaries until the Septimius Severus started recruiting the latter into the imperial guard at the end of the second century.17"

Page 9 of that same book.

During the later Marian Reforms the height requirements were extended to the rest of the legions including the auxiliaries. That book however doesn't cover that period.