The off-shell anomalous chromomagnetic dipole moment of the standard model quarks ($u$, $d$, $s$, $c$ and $b$), at the $Z$ gauge boson mass scale, is computed by using the $overline{textrm{MS}}$ scheme. The numerical results disagree with all the previous predictions reported in the literature and show a discrepancy of up to two orders of magnitude in certain situations.