The dependence of the ratio between the $B_s^0$ and $B^{+}$ hadron production fractions, $f_s/f_u$, on the transverse momentum ($p_T$) and rapidity of the $B$ mesons is studied using the decay channels $B_s^0\to J/\psi \varphi$ and $B^{+}\to J/\psi K^{+}$. The analysis uses a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment in 2018 and corresponding to an integrated luminosity of $61.6{\mathrm{fb}}^{-1}$. The $f_s/f_u$ ratio is observed to depend on the $B$ $p_T$ and to be consistent with becoming asymptotically constant at large $p_T$. No rapidity dependence is observed. The ratio of the $B^0$ to $B^{+}$ meson production fractions, $f_d/f_u$, is also measured, for the first time in proton-proton collisions, using the $B^0\to J/\psi K^{*0}$ decay channel. The result is found to be within 1 standard deviation of unity and independent of $p_T$ and rapidity, as expected from isospin invariance.