  We report the first measurement of the absolute branching fraction for
$\Lambda^+_{c}\rightarrow \Lambda \mu^+\nu_{\mu}$. 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 $\mathcal B({\Lambda^+_c\rightarrow
\Lambda \mu^+\nu_{\mu}})=(3.49\pm0.46({\rm stat})\pm0.27({\rm syst}))\%$. In
addition, we calculate the ratio $\mathcal{B}(\Lambda^+_c\rightarrow \Lambda
\mu^+\nu_{\mu})/\mathcal{B}(\Lambda^+_c\rightarrow \Lambda e^+\nu_{e})$ to be
$0.96\pm0.16({\rm stat})\pm0.04({\rm syst})$.
