The incident, which comes two days after Mr Singh asked agitating farmers in Mandsaur to 'practise yoga', took place when the union minster left the state guest house and was on his way to attend a programme on "Sabka Sath Sabka Bikas" in Jatani.
"Though the eggs did not hit the minister, one or two eggs fell in front of his vehicle," according to an eye witnesses.
The police arrested five Youth Congress workers including its state president Loknath Maharathy in this connection, senior police officer Satyabrata Bhoi said.
"Radha Mohan Singh has no moral right to remain in-charge of agriculture ministry after the killing of farmers in BJP ruled Madhya Pradesh," said Mr Maharathy before he was taken into custody.
Meanwhile, BJP strongly condemned the incident and blamed the state government for the incident.
"The Congress has lost its credibility across the country. I suspect the egg were hurled at the instance of the ruling BJD," Odisha BJP leader in-charge Arun Singh said.
However, senior Congress leader Pradeep Majhi said that "there is nothing wrong in the protest. The union government needs to know the sentiment of the people."
BJD vice-president Damodar Rout said, "Hurling eggs at the union minister will not help to solve any problem."
On Thursday, Mr Singh had attended a yoga event organised by Baba Ramdev.
The minister had said Yoga Guru Ramdev had invited him to Motihari for a three-day visit after a conversation on Mahatma Gandhi's Satyagrah at Champaran. When reporters asked him to comment on the death of five farmers in a firing in Mandsaur during a protest, the minister had replied, "Yoga kijiye (practice yoga)".
Hundreds of farmers have been protesting in Mandsaur demanding better prices for their crops and loan waivers.