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We present optical and near-infrared photometry of GRB~140606B ($z=0.384$),and optical photometry and spectroscopy of its associated supernova (SN). Theresults of our modelling indicate that the bolometric properties of the SN($M_{\rm Ni} = 0.4\pm0.2$~M$_{\odot}$, $M_{\rm ej} = 5\pm2$~M$_{\odot}$, and$E_{\rm K} = 2\pm1 \times 10^{52}$ erg) are fully consistent with thestatistical averages determined for other GRB-SNe. However, in terms of its$\gamma$-ray emission, GRB~140606B is an outlier of the Amati relation, andoccupies the same region as low-luminosity ($ll$) and short GRBs. The$\gamma$-ray emission in $ll$GRBs is thought to arise in some or all eventsfrom a shock-breakout (SBO), rather than from a jet. The measured peak photonenergy ($E_{\rm p}\approx800$ keV) is close to that expected for $\gamma$-rayscreated by a SBO ($\gtrsim1$ MeV). Moreover, based on its position in the$M_{V,\rm p}$--$L_{\rm iso,\gamma}$~plane and the $E_{\rmK}$--$\Gamma\beta$~plane, GRB~140606B has properties similar to both SBO-GRBsand jetted-GRBs. Additionally, we searched for correlations between theisotropic $\gamma$-ray emission and the bolometric properties of a sample ofGRB-SNe, finding that no statistically significant correlation is present. Theaverage kinetic energy of the sample is $\bar{E}_{\rm K} = 2.1\times10^{52}$erg. All of the GRB-SNe in our sample, with the exception of SN 2006aj, arewithin this range, which has implications for the total energy budget availableto power both the relativistic and non-relativistic components in a GRB-SNevent.

GRB 140606B / iPTF14bfu: Detection of shock-breakout emission from a cosmological gamma-ray burst?