This paper describes the first measurement of b-quark fragmentation fractions into bottom hadrons in Run II of the Tevatron Collider at Fermilab. The result is based on a 360  pb−1 sample of data collected with the CDF II detector in pp collisions at s√=1.96  TeV. Semileptonic decays of B0, B−, and B0s mesons, as well as Λ0b baryons, are reconstructed. For an effective bottom hadron pT threshold of 7  GeV/c, the fragmentation fractions are measured to be fu/fd=1.054±0.018(stat)+0.025−0.045(sys)±0.058(B), fs/(fu+fd)=0.160±0.005(stat)+0.011−0.010(sys)+0.057−0.034(B), and fΛb/(fu+fd)=0.281±0.012(stat)+0.058−0.056(sys)+0.128−0.087(B), where the uncertainty B is due to uncertainties on measured branching ratios. The value of fs/(fu+fd) agrees within one standard deviation with previous CDF measurements and the world average of this quantity, which is dominated by LEP measurements. However, the ratio fΛb/(fu+fd) is approximately twice the value previously measured at LEP. The approximately 2σ discrepancy is examined in terms of kinematic differences between the two production environments.