A very bright and fast varying gamma-ray flare has been detected from the blazar 3C 279 on June 16, 2015. We have studied the broadband spectral energy distribution of the source during the flaring episode and in the low activity state using a simple one zone leptonic model. We find that an electron energy distribution described by a broken power law can be used to reproduce the broadband emissions during the high and low activity states. The flux measurements at radio, infrared and optical frequencies are reproduced by the synchrotron emission resulting from the relativistic electrons in a jet magnetic field strength of 0.37 G. The gamma-ray emission from the blazar 3C 279 is attributed to the Comptonization of the IR seed photons from the dusty torus with a temperature of 870 K. The outburst from the source observed on June 16, 2015 can be ascribed to an efficient acceleration process associated with a sudden enhancement in the electron energy density in the emitting region with respect to the low activity state. The fast gamma-ray variability at a minute timescale implies that the emission during the flare originates from a more compact region and the size of the emission zone in the low activity state is found to be four times larger than that during the flare. We have also used the model parameters derived from the broadband spectral energy distribution modelling to investigate a few physical properties of the jet during the outburst.