The pressure dependence of the upper critical field, Hc2,c, of single crystalline FeSe was studied using measurements of the interplane resistivity, ρc, in magnetic fields parallel to tetragonal c axis. Hc2,c(T) curves obtained under hydrostatic pressures up to 1.56 GPa, the range over which the superconducting transition temperature, Tc, of FeSe exhibits a nonmonotonic dependence with local maximum at p1≈0.8 GPa and local minimum at p2≈1.2 GPa. The slope of the upper critical field at Tc,(dHc2,c/dT)Tc, also exhibits a nonmonotonic pressure dependence with distinct changes at p1 and p2. For pp2 the slope is in good semiquantitative agreement with a single band, orbital Helfand-Werthamer theory with Fermi velocities determined from Shubnikov–de Haas measurements. This finding indicates that Fermi surface changes are responsible for the local minimum of Tc(p) at p2≈1.2 GPa.