We present optical and near-infrared photometry of GRB 140606B (z = 0.384), and optical photometry and spectroscopy of its associated supernova (SN). The results of our modelling indicate that the bolometric properties of the SN (M Ni = 0.4 ± 0.2 M·, M ej = 5 ± 2 M·, and EK = 2 ± 1 × 10 52 erg) are fully consistent with the statistical averages determined for other γ -ray burst (GRB)-SNe. However, in terms of its γ -ray emission, GRB 140606B is an outlier of the Amati relation, and occupies the same region as low luminosity (ll) and short GRBs. The γ -ray emission in llGRBs is thought to arise in some or all events from a shock breakout (SBO), rather than from a jet. The measured peak photon energy (E p ≈ 800 keV) is close to that expected for γ -rays created by an SBO (≳ 1 MeV). Moreover, based on its position in theMV ,p-L iso,γ plane and the E K -Γβ plane, GRB 140606B has properties similar to both SBO-GRBs and jetted-GRBs. Additionally, we searched for correlations between the isotropic γ -ray emission and the bolometric properties of a sample of GRB-SNe, finding that no statistically significant correlation is present. The average kinetic energy of the sample is Ē K = 2.1 × 1052 erg. All of the GRB-SNe in our sample, with the exception of SN 2006aj, are within this range, which has implications for the total energy budget available to power both the relativistic and non-relativistic components in a GRB-SN event. © 2015 The Authors.