I know that in a photo diode current is carried by minority charge carriers whose concentration depends upon the incident light's intensity. I wonder if incident light has once created electron hole pairs and current has started to flow, how can the removal of incident light stop this current instantly?
There are two relevant mechanisms:
First, the intended one: Minority carriers, generated by light within or close to the p-n junction and therefore depletion region, reach one of the contacts and therefore are lost for additional transport. This is the contribution, which you can measure externally as generated current or voltage.
Second: Photo-generated carriers can also recombine due to scattering mechanisms and recombine with a carrier of opposite sign. Again, this particular carrier pair is lost for future transport. Scattering mechanisms could be crystal defects in the semiconductor material, impurities, phonon-assisted scattering due to elevated temperature, etc. Therefore, every material or heterostructure has some characteristic carrier life time, which determines the shut-off behavior in this case.