The influential think tank has forecast growth of just 2.4% in 2020, down from 2.9% in November.
But it said a longer “more intensive” outbreak could halve growth to 1.5%.
It came after the Bank of England vowed to help stabilise markets, which suffered steep losses last week.
Coronavirus is already forcing businesses to suspend operations in China and elsewhere as officials try to contain its spread.
The OECD forecast the global economy could recover to 3.3% growth in 2021, assuming the epidemic peaked in China in the first quarter of this year and other outbreaks proved mild and contained.
But it said the picture would be much worse if the virus spread throughout Asia, Europe and North America.
“The main message from this downside scenario is that it would put many countries into a recession, which is why we are urging measures to be taken in the affected areas as quickly as possible,” said Laurence Boone, the OECD’s chief economist.
Last week saw major stock markets suffer their worst weekly performance since the 2008 financial crisis, with $1.5 trillion being wiped off the value of global shares. Investors now hope central banks around the world will work in unison to support financial markets as the deadly virus spreads.
On Monday, the Bank of England said it continued to monitor developments and was assessing its potential impact on the global and UK economies and financial systems.
“The Bank is working closely with HM Treasury and the FCA (Financial Conduct Authority) – as well as our international partners – to ensure all necessary steps are taken to protect financial and monetary stability,” a spokesman said.
Japan’s central bank and the US Federal Reserve have also said they are prepared to intervene to stop more big falls on global stock markets.
Buoyed by the news, US stocks opened higher on Monday, with the Dow Jones Industrial Average and S&P 500 indexes both gaining 0.7%.
London’s FTSE 100 index closed 1.2% higher, while China’s Shanghai Composite index gained 3.2% and Japan’s benchmark index, the Nikkei 225, climbed 1%.