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 p (p) over bar collisions at root s = 1.96 TeV. Semileptonic decays of (B) over bar (0), B(-), and (B) over bar (0)(s) mesons, as well as Lambda(0)(b) baryons, are reconstructed. For an effective bottom hadron p(T) threshold of 7 GeV/c, the fragmentation fractions are measured to be f(u)/f(d)=1.054 +/- 0.018(stat)(-0.045)(+0.025)(sys)+/- 0.058(B), f(s)/(f(u)+f(d))=0.160 +/- 0.005(stat)(-0.010)(+0.011)(sys)(-0.034)(+0.057)(B), and f(Lambda b)/(f(u)+f(d))=0.281 +/- 0.012(stat)(-0.056)(+0.058)(sys)(-0.087)(+0.128)(B), where the uncertainty B is due to uncertainties on measured branching ratios. The value of f(s)/(f(u)+f(d)) 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 f(Lambda b)/(f(u)+f(d)) is approximately twice the value previously measured at LEP. The approximately 2 sigma discrepancy is examined in terms of kinematic differences between the two production environments. RI Ruiz, Alberto/E-4473-2011; Robson, Aidan/G-1087-2011; De Cecco, Sandro/B-1016-2012; Prokoshin, Fedor/E-2795-2012; Azzi, Patrizia/H-5404-2012