We report on a frequency measurement of the $(3{s}^{2})^{1}S_{0}\ensuremath{\rightarrow}(3s3p)^{3}P_{1}$ clock transition of $^{24}\mathrm{Mg}$ on a thermal atomic beam. The intercombination transition has been referenced to a portable primary Cs frequency standard with the help of a femtosecond fiber laser frequency comb. The achieved uncertainty is $2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$, which corresponds to an increase in accuracy of six orders of magnitude compared to previous results. The measured frequency value permits the calculation of several other optical transitions from $^{1}S_{0}$ to the $^{3}P_{J}$-level system for $^{24}\mathrm{Mg}$, $^{25}\mathrm{Mg}$, and $^{26}\mathrm{Mg}$. We describe in detail the components of our optical frequency standard such as the stabilized spectroscopy laser, the atomic beam apparatus used for Ramsey-Bord\'e interferometry, and the frequency comb generator and discuss the uncertainty contributions to our measurement including the first- and second-order Doppler effect. An upper limit of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ in $1\phantom{\rule{0.3em}{0ex}}\mathrm{s}$ for the short-term instability of our optical frequency standard was determined by comparison with a quartz oscillator disciplined to the signal received from the global positioning system (GPS).