We present Wide Field Camera 3 images taken with the Hubble Space Telescope within a single field in the southern grand design star-forming galaxy M83. Based on their size, morphology, and photometry in continuum-subtracted Hα, [S II], Hβ, [O III], and [O II] filters, we have identified 60 supernova remnant (SNR) candidates, as well as a handful of young ejecta-dominated candidates. A catalog of these remnants, their sizes and, where possible, their Hα fluxes are given. Radiative ages and pre-shock densities are derived from those SNRs that have good photometry. The ages lie in the range 2.62 < log (τrad/yr) < 5.0, and the pre-shock densities at the blast wave range over 0.56 < n 0/cm-3 < 1680. Two populations of SNRs have been discovered. These divide into a nuclear and spiral arm group and an inter-arm population. We infer an arm to inter-arm density contrast of 4. The surface flux in diffuse X-rays is correlated with the inferred pre-shock density, indicating that the warm interstellar medium (ISM) is pressurized by the hot X-ray plasma. We also find that the ISM in the nuclear region of M83 is characterized by a very high porosity and pressure, and infer an SNR rate of 1 per 70-150 yr for the nuclear (R < 300 pc) region. On the basis of the number of SNRs detected and their radiative ages, we infer that the lower mass of Type II SNe in M83 is M min = 16+7 –5 M . Finally, we give evidence for the likely detection of the remnant of the historical supernova, SN1968L.