We measure the masses of b hadrons in exclusively reconstructed final states containing a J/ψ→μ−μ+ decay using 220  pb−1 of data collected by the CDF II experiment. We find: m(B+)=5279.10±0.41(stat.)±0.36(sys.)  MeV/c2, m(B0)=5279.63±0.53(stat.)±0.33(sys.)  MeV/c2, m(B0s)=5366.01±0.73(stat.)±0.33(sys.)  MeV/c2, m(Λ0b)=5619.7±1.2(stat.)±1.2(sys.)  MeV/c2. m(B+)−m(B0)=−0.53±0.67(stat.)±0.14(sys.)  MeV/c2, m(B0s)−m(B0)=86.38±0.90(stat.)±0.06(sys.)  MeV/c2, m(Λ0b)−m(B0)=339.2±1.4(stat.)±0.1(sys.)  MeV/c2. The measurements of the B0s, Λ0b mass, m(B0s)−m(B0) and m(Λ0b)−m(B0) mass difference are of better precision than the current world averages