The exclusive photoproduction of $\mathrm {\Upsilon }\mathrm {(nS)} $ meson states from protons, $\gamma \mathrm {p} \rightarrow \mathrm {\Upsilon }\mathrm {(nS)} ,\mathrm {p}$ (with $\mathrm {n}=1,2,3$ ), is studied in ultraperipheral $\mathrm {p}$ Pb collisions at a centre-of-mass energy per nucleon pair of $\sqrt{\smash [b]{s_{{\mathrm {NN}}}}} = 5.02,\text {TeV} $ . The measurement is performed using the $\mathrm {\Upsilon }\mathrm {(nS)} \rightarrow \mu ^+\mu ^-$ decay mode, with data collected by the CMS experiment corresponding to an integrated luminosity of 32.6 $,\text {nb}^{-1}$ . Differential cross sections as functions of the $\mathrm {\Upsilon }\mathrm {(nS)} $ transverse momentum squared $p{\mathrm {T}} ^2$ , and rapidity y, are presented. The $\mathrm {\Upsilon (1S)}$ photoproduction cross section is extracted in the rapidity range $|y |< 2.2$ , which corresponds to photon–proton centre-of-mass energies in the range $91<W_{\gamma \mathrm {p}} <826,\text {GeV} $ . The data are compared to theoretical predictions based on perturbative quantum chromodynamics and to previous measurements.