The incident also drew flak from rival Congress-led UDF in Kerala.
Slamming the BJP-led government and RSS, Vijayan, who is a senior member of the CPI(M) politburo, said what happened in Bhopal was "unjustifiable".
He said it was a "reflection of culture" of the RSS and its affiliates.
Senior Congress leader and former Chief Minister Oommen Chandy described as "shocking and unfortunate" what Vijayan experienced in the BJP-ruled state and said it was a "naked violation of protocol" underlined in relations between the states in a federal structure.
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Noting that such incidents have "never ever" happened in Kerala, Vijayan said recently when Union Home Minister Rajnath Singh visited a village in politically volatile Kannur district in the midst of high tension due to political violence, no such incidents had occurred there.
"This is the difference in the mindset and culture," said Vijayan, terming the incident as a "bitter experience".
The chief minister alleged that the Madhya Pradesh police did not take action against the protesters as it was organised by RSS.
"We should see a cultural issue in it," Vijayan told reporters in Kochi.
The CPI(M) Kerala state secretariat described as "uncivilised" the alleged action of Madhya Pradesh government, its police and RSS in preventing the chief minister from attending the function.
The party alleged that the incident happened with the knowledge of the Madhya Pradesh Chief Minister and BJP's national leadership.