It has been recently predicted theoretically that due to nuclear motion light and heavy hydrogen molecules exposed to strong electric field should exhibit substantially different tunneling ionization rates [O. I. Tolstikhin, H. J. Worner, and T. Morishita, Phys. Rev. A 87, 041401(R) (2013)]. We studied that isotope effect experimentally by measuring relative ionization yields for each species in a mixed H_{2}/D_{2} gas jet interacting with intense femtosecond laser pulses. In a reaction microscope apparatus, we detected ionic fragments from all contributing channels (single ionization, dissociation, and sequential double ionization) and determined the ratio of total single ionization yields for H_{2} and D_{2}. The measured ratio agrees quantitatively with the prediction of the generalized weak-field asymptotic theory in an apparent failure of the frozen-nuclei approximation.