Lawyer Davinder Singh wrote to Roy Ngerng Yi Ling on Sunday asking him to take down the original article as well as the links posted on his Facebook pages and to post an apology by Wednesday.
Mr Singh said the allegations by Ngerng in his May 15 blog post were "false and baseless".
"The article means and is understood to mean that Mr Lee Hsien Loong, the Prime Minister of Singapore and the chairman of GIC, is guilty of criminal misappropriation of the monies paid by Singaporeans to the CPF (Central Provident Fund)," Singh wrote in the letter.
GIC is a sovereign wealth fund that manages more than $100 billion of the city-state's foreign reserves. CPF is the state pension fund.
Mr Singh said the post constituted a serious libel against Mr Lee, "disparages him, and impugns his character, credit and integrity".
Healthcare worker Ngerng, 33, regularly posts commentaries critical of the long-ruling People's Action Party (PAP) in his blog 'The Heart Truths'.
Recent posts have called for greater transparency on how CPF funds are invested by the government through GIC and state investment firm Temasek Holdings.
"My articles have been calling for greater accountability and transparency, and instead of acknowledging these issues, the prime minister has decided to sue me," Ngerng told AFP.
"I am quite disappointed and at this point I am still in discussion with my lawyer on my next course of action."