Former Morgan Stanley Asia Chairman Stephen Roach said the Federal Reserve is not equipped to help the economy during the coronavirus outbreak.

"Central banks are pulling out a playbook that was designed to deal with financial problems and not to deal with public health problems," Roach said on CNBC's "Squawk on the Street." "So I really think they're like a fish out of the water here. They have no idea how to contain or even to understand what may be about to happen in the public health area or the U.S. economy's response to that."

The Federal Reserve slashed its benchmark interest rate by 50 basis points on Tuesday morning, its first rate cut outside of a scheduled meeting since the financial crisis. The U.S. stock market, which rose strongly on Monday as expectations grew for central bank action, was volatile in the period following the cut.

The spread of coronavirus in the U.S. could lead to travel restrictions and a significant decrease in people going to public events, similar to what has happened in China, Roach said.

"We are not China, but we are going to be experiencing similar types of actions to deal with what the experts are saying is likely to be increased epidemic in the United States. These are actions that are insensitive to the level of interest rates which are already extraordinarily low," Roach said.

There are more than 91,000 confirmed cases of the virus around the world, including about 90 in the U.S. At least six people have died in the U.S.

Roach, who also served as Morgan Stanley's chief economist, said that the U.S. government's response to the outbreak has been "flailing" and that it needed to make significant investments in public health.

"We should be investing very heavily in building out our own public health infrastructure, rolling out massive testing on a scale we've never done before. We need to bring the scientists in, not the central bankers in, to design these programs. We do need to make sure there's ample support for liquidity for small- and medium-sized enterprises that might be hit," Roach said.