WASHINGTON—The U.S. government will postpone the April 15 tax-payment deadline for millions of individuals, giving Americans an additional 90 days to pay their 2019 income-tax bills in an unprecedented move intended to ease the economic pain inflicted by the coronavirus.

The IRS, using authority under President Trump’s national-emergency declaration, will waive interest and penalties as well, Treasury Secretary Steven Mnuchin said at the White House on Tuesday. The delay is available to people who owe $1 million or less and...