In this work, we investigate the next-to-leading order (NLO) QCD correction to $J/\ensuremath{\psi}$ associated production with a bottom quark pair from the Higgs boson decay within the nonrelativistic QCD framework. From numerical results, we find that the decay width of process $H\ensuremath{\rightarrow}b+J/\ensuremath{\psi}+\overline{b}$ at leading order (LO) mainly comes from the contribution of the Fock state ${^{3}S}_{1}^{(8)}$, and the NLO QCD corrections significantly enhance the decay width at LO accuracy by about two times. At NLO accuracy, the Fock states ${^{3}S}_{1}^{(8)}$ and ${^{3}P}_{J}^{(8)}$ channels give the main contribution, accounting for about 68% and 29% of the total decay width of $J/\ensuremath{\psi}$ associated production with a bottom quark pair at NLO accuracy from the Higgs boson decay, respectively. Considering the dominant contribution of color octet (CO) channels at NLO accuracy, the inclusive decay process $H\ensuremath{\rightarrow}b+J/\ensuremath{\psi}+\overline{b}+X$ has the potential to be found in future colliders with high energy/luminosity. The study of $J/\ensuremath{\psi}$ associated production with a bottom quark pair from the Higgs boson decay is not only useful to study the mechanism of color-octet, but also to assist in the investigation of the coupling for the Higgs boson with the bottom quark.