Thai shares and Singapore stocks fell 0.7% and 0.6%, respectively, making the them the top losers in the region.
Both Singapore and Thai economy have suffered following the outbreak, with Thailand expecting the number of foreign visitors to fall by 5 million this year, while Singapore lowered its 2020 growth target on Monday.
Apple Inc said it was unlikely to meet its sales outlook because of the epidemic, which has claimed more than 1,800 lives in mainland China and infected about 72,500 people.
The warning from the world's most valuable technology company could nudge markets to re-evaluate the macro impact of the epidemic, Maybank said in a note.
Financials stocks led losses in Singapore, with top lender DBS Group Holdings Ltd ticking down 0.6%.
Singapore Airlines lost up to 1.9% after it said it will temporarily cut flights across its global network in March, April and May due to weaker demand as a result of coronavirus.
The city-state is expected to roll out a hefty stimulus package at its annual budget later on Tuesday.
Consumer staples were top losers in Thailand, with convenience store operator CP All Pcl and sports drinks maker Osotspa Pcl falling up to 1% and 1.7%, respectively.
Bucking the trend, Indonesian equities rose on the back of gains in consumer staples and materials stocks.
"Investors are keeping an eye on the rate decision due on 20th February, " Hariyanto Wijaya, head of Investment Research at Mirae Asset Securities said.
Economists say poor growth data and impact of the virus outbreak on the economy may pressure the Indonesian central bank to start cutting interest rates again, following four rate cuts in 2019.
By Arundhati Dutta