[en] Highlights: • In the weak-magnetic-field approximation, we calculated the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in ${}^{27}$Al${}^{+}$ and ${}^{87}$Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=-1.183\left(6\right)\times {10}^{-3}$ for ${}^{27}$Al${}^{+}$ and $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=7.78\left(30\right)\times {10}^{-5}$ for ${}^{87}$Sr, agree with experimental values very well. • We also estimated the contributions from perturbing states to the $g$-factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. • The computational uncertainties were systematically analyzed. In the weak-magnetic-field approximation, we calculated the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in ${}^{27}$Al${}^{+}$ and ${}^{87}$Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=-1.183\left(6\right)\times {10}^{-3}$ for ${}^{27}$Al${}^{+}$ and $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=7.78\left(30\right)\times {10}^{-5}$ for ${}^{87}$Sr, agree with experimental values very well. The influence of relativistic effects and electron correlations on the involving hyperfine interaction and Zeeman matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the $g$-factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. Based on these, the computational uncertainties were systematically analyzed for the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in these two atomic systems.