Photoluminescence (PL) spectroscopy has been performed on a set of self‐assembled InSb, GaSb, and AlSb quantum dot (QD) heterostructures grown on GaAs. Strong emission bands with peak energies near 1.15 eV and linewidths of ∼80 meV are observed at 1.6 K from 3 monolayer (ML) InSb and GaSb QDs capped with GaAs. The PL from a capped 4 ML AlSb QD sample is weaker with peak energy at 1.26 eV. The PL bands from these Sb‐based QD samples shift to lower energy by 20–50 meV with decreasing excitation power density. This behavior suggests a type II band lineup. Support for this assignment, with electrons in the GaAs and holes in the (In,Ga,Al)Sb QDs, is found from the observed shift of GaSb QD emission to higher energies when the GaAs barrier layers are replaced by Al0.1Ga0.9As.