The video, which has gone viral on social media, was shared on Twitter by BJP national general secretary Kailash Vijayvargiya.
However, Congress leader Sachin Pilot said in Mumbai his party will never instigate violence for political benefits and demanded that the video should be investigated for authenticity.
The video was shot last evening when Congress MLA Shakuntala Khatik, who represents Karera Assembly segment, was staging a protest at Karera police station in Shivpuri district against the killing of farmers in Mandsaur.
This irked Khatik, who later sat on a protest at the police station along with her supporters and the video was shot during the sit-in.
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The video shows the MLA purportedly asking her supporters to set the police station on fire.
"Thane ko jala do (torch the police station)," she was heard shouting in the video.
District Congress spokesman Harvir Singh Raghuvanshi said that the policemen threw water on the MLA during a protest organised against the killing of farmers in police firing in Mandsaur.
Pilot said, "We are not a party that will instigate violence for political benefits, not at all... We will never accept the way of violence to force the government into submission."
He said the party has no qualms in "wholeheartedly" supporting a legitimate demand of anyone and ensuring that it is fulfilled.
"We are a democratic party. We believe in those principles. If this particular video... Is out there, I think someone can really verify and see if it is true or not," Pilot said.
Reacting to the video, state BJP spokesman and Bhopal MP Alok Sanjar said the incident showed that the Congress believed in violence.
"This video shows that the Congress is inciting people to set ablaze government property. This is the dirty politics of the Congress to meet their selfish ends. This shows the true character of the Congress," Sanjar said.
Parts of western Madhya Pradesh has been on the boil ever since the farmers launched an agitation last week seeking loan waiver and better crop prices.
A 26-year-old farmer died yesterday in Badavan village of violence-hit Mandsaur district, with people in that area alleging that he was beaten up by policemen.
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