The farmers say that they have not been adequately compensated for the land that was given to race organisers to build the $350-million circuit in Greater Noida, on the outskirts of New Delhi.
Excitement has been building in India ahead of the big race on October 30.
"We are not against the race, but we feel we have been short-changed in the deal," farmer leader Virender Dhada said.
"We will stage protest marches and sit-ins next to the track starting October 23 to ensure our voice is heard."
Farmers are demanding more compensation and employment opportunities because they claim their livelihood has been snatched away along with their land to build the Buddh International Circuit.
"We are only demanding what is our right. The authorities have been turning a deaf ear to our legitimate demands. If they are willing to talk to us even now, we will stop the planned agitation," Dhada said.
JP Sports, organisers of the race, dismissed the threat as blackmail tactics aimed at gaining publicity.
"This whole thing is a big joke," said an executive from the company who did not want to be named.
"People should not be taking these threats seriously. There is so much riding on the race for the company and the country, do you think we will allow a handful of farmers to spoil it?
"We have spent $400 million dollars on the race and we will spend a few millions more if needed to have adequate security in place. We will do whatever it takes to have a wonderful event."