The first measurements of the top- and antitop-quark differential production cross sections and the top-quark charge asymmetry in the forward region are presented, using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 5.4 fb^{-1}. The total production cross sections of top and antitop quarks are also determined. Measurements are performed using the μ+b-jet final state within a fiducial region defined by b-jet p_{T,jet}>50 GeV and pseudorapidity 2.2<η_{jet}<4.0, with the muon from the W-boson decay required to have p_{T,μ}>25 GeV and 2.0<η_{μ}<4.5. The muon and b-jet system must satisfy p_{T}(μ+jet)>20 GeV. The measured integrated production cross sections for the top and antitop quarks are σ_{t}=0.95±0.04±0.08±0.02 pb, σ_{t[over ¯]}=0.81±0.03±0.07±0.02 pb, where the first uncertainty is statistical, the second systematic, and the third accounts for the luminosity uncertainty. The top-quark charge asymmetry is measured to be A_{C}^{t}=0.08±0.03±0.01, where the first uncertainty is statistical and the second is systematic. These results are consistent with next-to-leading order Standard Model predictions.