"We've lived all three phases of this crisis," he said on CNBC's "Squawk on the Street." "Our China business is coming back."
McCormick, the maker of Old Bay Seasoning, French's mustard and Frank's Red Hot, has three plants in China, including one in the city of Wuhan in Hubei province, Kurzius said. The coronavirus originated in Wuhan late last year.
"All of our facilities are open. People are back at work. We're operating normally," he said.
Retail demand from consumers is "through the roof," Kurzuis said, but he cautioned that not everything has gone back to normal. He said the company's food service business is recovering at a slower pace.
"Quick service restaurants and regular food service restaurants are open largely, but customer traffic is building. It's going to take a while for that to rebuild," he said.
Kurzius' insight into how McCormick's China business is recovering from the outbreak fallout comes during a debate over the Chinese government's transparency around the crisis.
Bloomberg recently reported that U.S. intelligence officials told the White House that China deliberately downplayed the scale of the outbreak, limiting the reported number of confirmed cases and deaths.
There have been more than 82,400 confirmed cases in China and 3,322 deaths, according to composite data Thursday morning from Johns Hopkins University. Chinese health officials also have reported a step decline in new cases over the last few weeks.
But Kurzius is among other business leaders who say the situation on the ground in China has improved. Starbucks has reopened around 95% of the stores it temporarily shuttered in China in response to the virus' spread, CEO Kevin Johnson told CNBC last week.
McCormick saw a dramatic increase in U.S. sales in March, Kurzius said, as the threat of the coronavirus intensified and stay-at-home orders were put in place for millions of Americans.
Kurzius, who has served in various roles for McCormick since joining in 2003, said the company's consumer business sales through stores increased by 75% in "the first part of March." That segment accounts for about 80% of McCormick's business.
The increase is "just incredible in a business where single-digit gains are considered exciting," he said, attributing the spike in sales to people being at home and needing, for example, to make meals for their families.
"You wouldn't believe the number of requests we've gotten for recipes for slime," he said. "Our recipe mixes are up over 100%. It's a staggering thing."
Sales of Frank's Red Hot, which McCormick acquired in 2017, are up more than 100% in March, he said. French's mustard, which also was part of the $4.2 billion deal with Reckitt Benckiser Group, has seen a similar increase.
"This is a great time to be in those businesses," he said.