Blazars, a class of highly variable active galactic nuclei, sometimes exhibit Orphan $gamma$-ray flares. These flares having high flux only in $gamma$-ray energies do not show significant variations in flux at lower energies. We study the temporal and spectral profile of these Orphan $gamma$-ray flares in detail from three $gamma-ray$ bright blazars, 3C 273, PKS 1510-089 and 3C 279 and also their simultaneous broadband emissions. We find that the variability timescales of the Orphan $gamma$-ray flares were $(0.96pm0.28)$ days, $(3.12pm2.40)$ hr and $(2.16pm0.72)$ hr, for 3C 273, PKS 1510-089 and 3C 279, respectively. The broadband spectral energy distributions (SEDs) during these flares have been modelled with a leptonic model from two emission regions. This model suggests that Orphan $gamma$-ray flares might have originated from inverse Compton scattering of relativistic electrons by the seed photons from the broad-line region or dusty torus, which is the first region. While the second broader region, lying further down the jet, could be responsible for X-ray and radio emissions. The possible locations of these emission regions in the jets of the three sources have been estimated from SED modelling.