A search for the standard model (SM) Higgs boson decaying to two muons is presented using data recorded by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13~\mathrm{TeV}, corresponding to an integrated luminosity of 35.9~\mathrm{fb}^{-1}. Limits are set on the cross section of the Higgs boson decaying to two muons for mass hypotheses between $120$ and 130~\mathrm{GeV}. For a Higgs boson with a mass of 125~\mathrm{GeV} decaying to two muons, the $95\%$ confidence level (CL) observed (expected) upper limit on the production rate is found to be $2.64$ ($2.08$) times the SM value. The combination with data recorded at center-of-mass energies of $7$ and 8~\mathrm{TeV} yields a $95\%$ CL observed (expected) upper limit of $2.64$ ($1.89$) times the SM value. This corresponds to an upper limit on the Higgs boson branching fraction to muons of $5.7\times10^{-4}$, assuming the SM production cross sections.

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