"Either it is a tongue in cheek comment by the Prime Minister and he really did not mean what he said, or he actually does not know what he is saying," Mr Singh, who is also a key leader of the Congress in Punjab, said a written statement.
The Prime Minister's praise for Mr Badal was made at a function -- to mark the 113th birth anniversary of Jai Prakash Narayan -- where he felicitated public personalities for fighting the Emergency imposed by the Indira Gandhi regime.
In what seemed to be a reference to the Gandhi family, PM Modi said: "There is a special family about whom pages are written in history even if their fingernails break. Very few people know that Badal Saheb is Nelson Mandela of India, who has spent nearly two decades in jail only because of political differences."
Almost immediately, the Prime Minister's comment became a target of jokes under the hashtag # #YoBadalSoMandela.
Mandela died all over again today. The Mandela-Badal comparison by PM Modi shameful. https://t.co/CPq48rHKBH- Priyanka Chaturvedi (@priyankac19) October 11, 2015
In a contest: Teacher:- Who is CM of Punjab All Students: Prakash Singh Badal Bal Narendra : Nelson Mandela (Wins) #YoBadalSoMandela- Swapnil Kadam (@swapn_7) October 11, 2015
Calling it an insult, Mr Singh said, "If Mr Modi seriously means Mr Badal to be the Nelson Mandela of India, then, I am sure, he might be thinking that like Mandela he (Mr Badal) deserves a Bharat Ratna and Nobel Peace Prize also and he should really lobby for him".
President of Punjab Pradesh Congress Committee, Partap Singh Bajwa, tweeted:
The Prime Minister's political archrival, Delhi Chief Minister Arvind Kejriwal tweeted:
Dear PM please have some pity on the legendary Nelson Mandela. Don't compare him with Alibaba of Punjab. #YoBadalSoMandela- Partap Singh Bajwa (@Partap_Sbajwa) October 11, 2015
Badal is the Nelson Mandela of India?- Arvind Kejriwal (@ArvindKejriwal) October 11, 2015