We make use of the Hubble Space Telescope proper-motion catalogs derived by to produce the first radial velocity-dispersion profiles \sigma ( R ) for blue straggler stars ( BSSs ) in Galactic globular clusters ( GCs ) , as well as the first dynamical estimates for the average mass of the entire BSS population . We show that BSSs typically have lower velocity dispersions than stars with mass equal to the main-sequence turnoff mass , as one would expect for a more massive population of stars . Since GCs are expected to experience some degree of energy equipartition , we use the relation \sigma \propto M ^ { - \eta } , where \eta is related to the degree of energy equipartition , along with our velocity-dispersion profiles to estimate BSS masses . We estimate \eta as a function of cluster relaxation from recent Monte Carlo cluster simulations by and then derive an average mass ratio M _ { \mathrm { BSS } } / M _ { \mathrm { MSTO } } = 1.50 \pm 0.14 and an average mass M _ { \mathrm { BSS } } = 1.22 \pm 0.12 M _ { \odot } from 598 BSSs across 19 GCs . The final error bars include any systematic errors that are random between different clusters , but not any potential biases inherent to our methodology . Our results are in good agreement with the average mass of M _ { \mathrm { BSS } } = 1.22 \pm 0.06 M _ { \odot } for the 35 BSSs in Galactic GCs in the literature with properties that have allowed individual mass determination .