The \(D^+_s\to K^+K^-\mu^+\nu_\mu\) decay is studied based on 7.33 fb\(^{-1}\) of \(e^+e^-\) collision data collected with the BESIII detector at center-of-mass energies in the range from 4.128 to 4.226 GeV. The absolute branching fraction is measured as \({\mathcal B}(D^+_s\to \phi \mu^+\nu_\mu) = (2.25\pm 0.09 \pm 0.07) \times10^{-2}\), the most precise measurement to date. Combining with the world average of \({\mathcal B}(D^+_s\to \phi e^+\nu_e)\), the ratio of the branching fractions obtained is\(\frac{{\mathcal B}(D^+_s\to \phi \mu^+\nu_\mu)}{{\mathcal B}(D^+_s\to \phi e^+\nu_e)} = 0.94\pm0.08\), in agreement with lepton universality. By performing a partial wave analysis, the hadronic form factor ratios at \(q^{2}=0\) are extracted, finding \(r_{V}=\frac{V(0)}{A_{1}(0)}=1.58\pm0.17\pm0.02\) and \(r_{2}=\frac{A_{2}(0)}{A_{1}(0)}=0.71\pm0.14\pm0.02\), where the first uncertainties are statistical and the second are systematic. No significant \(S\)-wave contribution from \(f_0(980)\to K^+K^-\) is found. The upper limit \(\mathcal{B}(D_s^+\to f_0(980)\mu^{+}{\nu}_{\mu}) \cdot{\mathcal B}(f_0(980)\to K^+K^-) < 5.45 \times 10^{-4}\) is set at 90\% confidence level.