The police say the attacker is 18-year-old Vijay Meena and he has been arrested on charges of hurting religious sentiment, breaking peace, promoting enmity and causing hurt. The video was allegedly recorded on Monday night and circulated by him.
In the three-minute clip, Vijay Meena is seen slapping Mohammad Salim 25 times while trying to get him to say "Jai Shri Ram". The 45-year-old responds: "Parvardigaar sabse bada hai (God is almighty)."
The incident took place on a road around 30 km from Mount Abu, a popular tourist spot in the state.
After watching the video, Muslim leaders filed a complaint against Vijay Meena.
On December 6, one Mohammad Afrazul was hacked to death and burnt in Rajsamand in Rajasthan. A gruesome video of the crime went viral.
Last year, Pehlu Khan, 55, died in Alwar after being brutally beaten up by cow vigilantes on suspicion of cattle smuggling.
State home minister Gulab Chand Kataria said: "The police always takes action when such incidents are reported. In this case also we have taken action and in the past too, the police has acted upon such type of incidents."