The decay width and mass of the Ds1(2536)+ meson are measured via the decay channel Ds1+ -> D*+KS0 using 385 fb^-1 of data recorded with the BABAR detector in the vicinity of the Y(4S) resonance at the PEP-II asymmetric-energy electron-positron collider. The result for the decay width is 0.92 +- 0.03 (stat) +- 0.04 (syst) MeV. For the mass, a value of 2535.08 +- 0.01 +- 0.15 MeV/c^2 is obtained. The mass difference between the Ds1+ and the D*+ is measured to be 524.83 +- 0.01 +- 0.04 MeV/c^2, representing a significant improvement compared to the current world average. The unnatural spin-parity assignment for the Ds1+ meson is confirmed.