The ministry said earlier this week that it "instructed" the government office responsible for implementing the 2019 Protection from Online Falsehoods and Manipulation Act "to issue correction directions" to the Singapore People's Party (SPP) and leader Goh Meng Seng.
The order covered Goh's and the SPP's posts "implying that Covid-19 vaccination had caused or substantially contributed to" a case of stroke and the separate death of an 81-year-old.
The ministry said the death was caused by heart disease and the stroke case was "highly unlikely to be related to the Covid-19 vaccination."
The correction demand also applied to the Facebook page of Singapore Uncensored, a news and comment website which also posted the claims.
Around 60,000 coronavirus cases have been reported in Singapore, almost all of which date to an outbreak last year among migrant workers.
Thirty virus-linked deaths have been confirmed in the city-state of 5.7 million, where over 500,000 people have been vaccinated.
The government said in February that anyone suffering severe side effects after vaccination would be entitled to financial compensation.
Facebook's Asia regional headquarters is in Singapore, which despite its small size regularly features among the world's top 10 foreign investment destinations, according to data put together by the United Nations Conference on Trade and Development (UNCTAD). - dpa