The diffractive production of ρ0(770) mesons in muon-proton interactions is studied in the kinematic region 0.15 GeV2 < Q2 < 20 GeV2 and 20 GeV < v < 420 GeV. The data were obtained in the Fermilab fixed-target experiment E665 with primary muons of 470 GeV energy. Results are presented on the Q2, x and v dependence of the cross section, on the shape of the π+π- mass spectrum, on the slope of the diffraction peak and on the production and decay angular distributions of the ρ0(770). The cross section for diffractive production of ρ0 by virtual photons on protons depends mainly on Q2. At fixed Q2, no significant dependence on x or v is observed. The extrapolation to Q2 = 0 yields a photoproduction cross section of (10.30 ± 0.33) μb. The slope of the t′ distribution has a value of (7.0 ± 0.2) GeV-2, with a tendency to decrease as Q2 increases. The production and decay angular distributions of the ρ0 depend strongly on Q2 and are consistent with s-channel helicity conservation. The ratio R = σL/σT deduced from the decay angular distributions rises strongly with Q2, passing the value of 1 at Q2 ≈ 2 GeV2.