We report the first measurement of the absolute branching fraction for $Λ^+_{c}→ Λ μ^+ν_{μ}$. This measurement is based on a sample of $e^+e^-$ annihilation data at a center-of-mass energy of $\sqrt{s}=4.6$ GeV collected with the BESIII detector at the BEPCII storage rings. The sample corresponds to an integrated luminosity of 567 pb$^{-1}$. The branching fraction is determined to be $\mathcal B({Λ^+_c→ Λ μ^+ν_{μ}})=(3.49±0.46({\rm stat})±0.27({\rm syst}))\%$. In addition, we calculate the ratio $\mathcal{B}(Λ^+_c→ Λ μ^+ν_{μ})/\mathcal{B}(Λ^+_c→ Λ e^+ν_{e})$ to be $0.96±0.16({\rm stat})±0.04({\rm syst})$.