Officials have confirmed that the video was taken on June 17, somewhere in the Visavadar tehsil of Junagadh district in Gujarat's Saurashtra region.
AP Singh, a top forest department official in the Junagarh Wildlife circle told news agency Press Trust of India that the four men were traced by forest officials to Bhavnagar district 100 km away and arrested for endangering the life of a lion cub.
"We also seized their car. We will seek their remand from court to investigate their motive behind this act," Mr Singh said.
In the cell phone footage that sparked outrage among wildlife enthusiasts, one of the occupants of the car is heard exhorting the driver to go faster. "Increase the speed... Hit it... Increase the speed. Shoot it. Shoot it. Won't get such a chance," he is heard saying in Gujarati.
"We learned that when they said 'shoot it,' they meant shooting video of the cub on their mobile phone, not shooting the cub with a gun," Mr Singh said, according to PTI.
The location where the incident took place is close to the Gir Wildlife Sanctuary spread across 1400 square km, the only remaining home of the Asiatic lion
Two months ago, people driving through Amreli on the Pipavav-Rajula highway, were greeted by the sight of a pride of lions crossing the road. Many lions have died in road and train accidents in the area.