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The $^{8}\mathrm{B}+^{51}\mathrm{V}$ elastic scattering at ${E}_{\mathrm{lab}}=22$ MeV was measured using a $^{8}\mathrm{B}$ secondary beam produced and selected by the RIBRAS (Radioactive Ion Beams in Brasil) system. An elastic scattering angular distribution was obtained and analyzed within the optical model, using a Woods-Saxon form factor. A full continuum discretized coupled-channels calculation was performed to take into account the effect of the $^{8}\mathrm{B}\ensuremath{\rightarrow}^{7}\mathrm{Be}+p$ elastic breakup on the elastic scattering dynamics. The breakup and total reaction cross sections obtained from these analyses are also presented.