Singaporean stocks closed down 2.6%, weighed down by losses in heavyweight conglomerates Jardine Cycle & Carriage Ltd and Jardine Strategic Holdings Ltd.
Singapore will close schools and most workplaces, except for essential services like supermarkets and banks for a month, as its infections have been rising sharply in recent weeks.
Elsewhere, Benchmark Brent crude oil futures rose above $30 a barrel on Friday after soaring as much as 47% in the previous session, on expectations of a huge global supply cut deal to support prices.
Thailand stocks closed marginally higher and posted its best week since October 2015. Energy heavyweights PTT and PTT Exploration and Production gained over 5% each.
Also aiding Thai sentiment was Deputy Prime Minister Somkid Jatusripitak's statement that new economic measures to ease virus impact would be worth 10% of GDP.
Shares in Vietnam added over 3%, boosted by gains in the real estate sector.
The Philippines, the world's top rice buyer, said on Thursday it has secured Vietnam's commitment for continuous supply of the staple food, which may include a 300,000-tonne importation.
Vietnamese markets were closed on Thursday for a holiday.
Indonesian equities gained 2%, with financials boosting the index. PT Bank Mandiri (Persero) Tbk and PT Bank Negara Indonesia (Persero) Tbk rose 5.8% and 4.2%, respectively.
Indonesian palm producers have no plans to reduce workers' hours or other activities despite virus, an industry body said on Friday.
Indonesia is the world's largest producer of palm oil.
Shares in Malaysia and the Philippines ended flat.
By Arundhati Dutta