We report on damage to DNA in an aqueous medium induced by ultrashort pulses of intense laser light of 800 nm wavelength. Focusing of such pulses, using lenses of various focal lengths, induces plasma formation within the aqueous medium. Such plasma can have a spatial extent that is far in excess of the Rayleigh range. In the case of water, the resulting ionization and dissociation gives rise to in situ generation of low-energy electrons and OH-radicals. Interactions of these with plasmid DNA produce nicks in the DNA backbone: single strand breaks (SSBs) are induced as are, at higher laser intensities, double strand breaks (DSBs). Under physiological conditions, the latter are not readily amenable to repair. Systematic quantification of SSBs and DSBs at different values of incident laser energy and under different external focusing conditions reveals that damage occurs in two distinct regimes. Numerical aperture is the experimental handle that delineates the two regimes, permitting simple optical control over the extent of DNA damage.