"If this is not contained within the next few months, we will see a big shrinking in the economy because, imagine a country like China, its people not able to go and travel and do commerce and do deals," he told CNBC's Hadley Gamble on Wednesday.
The novel coronavirus was first detected in the Chinese city of Wuhan in late 2019, and infections have been reported in more than 30 countries.
China has confirmed over 78,000 cases and 2,700 deaths, while South Korea, Italy and Iran have seen spikes in cases. These countries have been the targets of travel advisories and, in some cases, bans.
"Imagine a company like Huawei, who now cannot go and serve its clients," said Sawiris, who was formerly chief executive of Orascom Telecom. "It's going to be a big impact."
Noting that many people cross the border between Italy and Switzerland for work, he said it would be a "worrying situation" if the former has to close its borders.
He also warned that Africa would not be able to contain the situation if the virus reaches the continent.
"If for any reason this virus spreads to Africa, they're totally unprepared for this," he said. "(They) don't even have hospitals to treat the normal influenza."
"I'm feeling that if they don't come up with antidotes and the vaccine very, very soon, for sure, the economy of the whole world will shrink," he said.
Separately, Sawiris weighed in on the death of former Egyptian president Hosni Mubarak.
"(His) legacy is the stability we had, the opening up of the economy from a market closed economy, to an open economy," he said.
While those who were part of the 2011 revolution that ousted Mubarak feel they were not on the same page as him, Sawiris said people in the country are "a little bit sad" that he has died. Egypt has announced three days of mourning.
"As an Egyptian I'm saddened because he was not an evil man, he was a good man."
– CNBC's Natasha Turak contributed to this report.