We study theoretically the strong-field absorption of an ultrafast optical pulse by a gapped graphene monolayer. At low field amplitudes, the absorbance in the pristine graphene is equal to the universal value of $2.3$ percent. Although the ultrafast optical absorption for low field amplitudes is independent of the polarization, linear or circular, of the applied optical pulse, for high field amplitudes, the absorption strongly depends on the pulse polarization. For a linearly polarized pulse, the optical absorbance is saturated at the value of $approx 1.4$ percent for the pulses amplitude of $geq 0.4~mathrm{V/AA}$, but no such saturation is observed for a circularly polarized pulse. For the gapped graphene, the absorption of a linearly polarized pulse has a weak dependence on the bandgap, while for a circularly polarized pulse, the absorption is very sensitive to the bandgap. %Opening a bandgap in graphene by placing in on, for example, SiC substrate strongly modify the ultrafast absorption at small field amplitudes.
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