We present the results of a search for heavy QCD axions performed by the ArgoNeuT experiment at Fermilab. We search for heavy axions produced in the NuMI neutrino beam target and absorber decaying into dimuon pairs, which can be identified using the unique capabilities of ArgoNeuT and the MINOS near detector. This decay channel is motivated by a broad class of heavy QCD axion models that address the strong CP and axion quality problems with axion masses above the dimuon threshold. We obtain new constraints at a 95% confidence level for heavy axions in the previously unexplored mass range of 0.2-0.9 GeV, for axion decay constants around tens of TeV.