The U.S. is not prepared for what is coming as COVID-19 spreads rapidly across the country, public health and infectious disease specialist Michael Osterholm told CNBC on Tuesday.

The virus has surpassed the containment stage, he said, and the U.S. government is not responding appropriately for the magnitude of spread the country will likely see.

"Right now we're approaching this like it's the Washington, D.C., blizzard — for a couple days we're shut down," the director of the Center for Infectious Disease Research and Policy at the University of Minnesota said in a "Squawk Box" interview. "This is actually a coronavirus winter and we're in the first week."

The U.S. is not containing the virus, Osterholm added, warning that it is substantially more contagious than some U.S. officials have warned. He said the most important thing is to protect people who are most at risk of dying from the virus, mostly older people and those with underlying health conditions.

"This is just going to keep spreading. We have to stop fooling people into thinking this is only by close contact where I have to be within 2 or 3 feet. We're going to see much more transmission," he said. "There will be widespread transmission of this virus around the country, and what we have to do is keep people who are at high risk of having bad outcomes, older, underlying health conditions, from being exposed."

COVID-19 has infected more than 755 Americans, according to Johns Hopkins University, and killed at least 26. Johns Hopkins' data shows that the virus has spread to more than half of the states.