Measurements of the total and differential cross sections dσ/dp(T)(B) and dσ/dy(B) for B(+) mesons produced in pp collisions at sqrt[s]=7 TeV are presented. The data correspond to an integrated luminosity of 5.8 pb(-1) collected by the CMS experiment operating at the LHC. The exclusive decay B(+)→J/ψK(+), with J/ψ→μ(+)μ(-), is used to detect B(+) mesons and to measure the production cross section as a function of p(T)(B) and y(B). The total cross section for p(T)(B)>5 GeV and |y(B)|<2.4 is measured to be 28.1±2.4±2.0±3.1 μb, where the first uncertainty is statistical, the second is systematic, and the last is from the luminosity measurement.