"Thaaney mein aag lagaa do (burn down the police station)," Shakuntala Khatik is heard saying more than once as she shouts slogans with the protesters, who were reportedly angry at being stopped and restrained by the police.
BJP spokesperson Tajinder Bagga posted the video in a tweet calling the comment "shameful"; the post was re-tweeted 1,200 times in two hours.
Ms Khatik is from the Shivpuri district, which is about 300 km from Mandsaur, the epicenter of violent protests by farmers demanding better prices for their produce and debt relief.
Yesterday, Congress vice president Rahul Gandhi provoked a five-hour showdown with the police in Rajasthan and Madhya Pradesh as he tried to go to Mandsaur to meet the families of five farmers killed in police firing on Tuesday.
The protests, which started over a week ago, escalated after the farmer deaths. Ms Khatik was leading one of the many marches in parts of Madhya Pradesh.