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-circle dot, M-ej = 5 +/- 2 M-circle dot, and E-K = 2 +/- 1 x 10(52) erg) are fully consistent with the statistical averages determined for other gamma-ray burst (GRB)-SNe. However, in terms of its gamma-ray emission, GRB 140606B is an outlier of the Amati relation, and occupies the same region as low luminosity (ll) and short GRBs. The gamma-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 approximate to 800 keV) is close to that expected for. -rays created by an SBO (greater than or similar to 1 MeV). Moreover, based on its position in the M-V,M- (p)- L-iso,L-gamma plane and the E-K-Gamma eta plane, GRB 140606B has properties similar to both SBO-GRBs and jetted-GRBs. Additionally, we searched for correlations between the isotropic gamma-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 (E) over bar (K) = 2.1 x 10(52) 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.