The emergency package includes low-cost loans, grants and technical assistance.
The action comes as leaders around the world pledge to shield their countries from the economic impact of the outbreak.
It follows warnings that slowdown from the outbreak could tip countries into recession.
The aid is intended to help countries improve their public health response to the crisis, as well as work with the private sector to reduce the economic impact.
The organisation said it would prioritise the poorest and most at-risk countries in distributing the aid to counter the effects of the virus, which has spread to more than 70 countries around the world.
Half of the package comes from the bank’s International Finance Corporation, which works with the private sector. About $4bn of the $12bn is being shifted from previously available funds.
What do I need to know about the coronavirus?
Authorities have confirmed more than 92,000 cases of the virus worldwide of which more than 80,000 are in China. More than 3,000 people have died globally, the vast majority in China.
New infections and deaths have been declining in recent weeks in China due to draconian quarantine measures. The country on Wednesday reported 38 more deaths but a fall in fresh cases for a third consecutive day.
The worst-hit country outside China remains South Korea which on Wednesday reported 516 new confirmed infections, bringing the total to 5,328. The country’s death toll stands at 33.
“The point is to move fast; speed is needed to save lives,” Mr Malpass said in conference with reporters. “There are scenarios where much more resources may be required. We’ll adapt our approach and resources as needed.”
The Dow Jones shed nearly 800 points on Tuesday, paring Monday’s big gains. This was despite a rare emergency move by the US Federal Reserve to cut interest rates by 0.5% amid fears over the impact of the coronavirus.
It was the biggest cut since the global financial crisis more than a decade ago.