Johnson & Johnson's chief scientific officer, Dr. Paul Stoffels, told CNBC on Monday that he believes the drugmaker can create a vaccine in the coming months to fight against the fast-spreading coronavirus.

But he said it could take up to a year to bring it to market.

"We have dozens of scientists working on this so we're pretty confident we can get something made that will work and stay active for the longer term," said Stoffels, also vice chairman of the executive committee, in a "Squawk Box" interview.

"We'll see in the next few weeks how this goes," he added. Stoffels confirmed the company started working on a coronavirus vaccine two weeks ago.

Chinese officials said there are now more than 2,800 confirmed cases of the flu-like coronavirus, with the death toll rising to 81. It was first identified in the city of Wuhan in Hubei province last month.

More countries are also reporting coronavirus cases, including the U.S., which on Sunday confirmed a fifth case.

The new strain comes from a large family of viruses known as coronaviruses, according to the World Health Organization. They are known to cause illness ranging from the common cold to more severe diseases such as the 2002-2003 outbreak of SARS, or severe acute respiratory syndrome.

Stoffels said the pharmaceutical company needed to start from scratch on this vaccine, much like how it operated in the Zika outbreak. Though Johnson & Johnson could shave two to three months off of that due to technological advances, he said.

"We are going to take an approach with at least five different constructs and different partners and collaborations all over the world in order to see which part of the virus we can use to make an effective vaccine and develop a model that we can invest in," he added.

Drugmaker Moderna also told CNBC last week that it is working with U.S. government health agencies to develop a vaccine for the current strain of coronavirus.

Fred Hassan, former CEO of Schering-Plough, said later on "Squawk on the Street" that Stoffels' estimate on when Big Pharma might have a vaccine ready for market is accurate. "I believe we'll get the thing done in less than a year."

Hassan also pointed to new technology and scientific advances as factors helping streamline vaccine efforts.﻿

Several companies, including Walt Disney with its Shanghai Disney, are suspending operations until further notice during the normally festive weeklong Lunar New Year holiday to prevent the outbreak from spreading. Starbucks and McDonald's also closed stores in Hubei province.

Authorities also temporarily banned the trade of wild animals in China on Sunday, responding to the outbreak as some consider the virus to have originated in a type of wild animal sold and consumed as food in Wuhan.

Investors worldwide have been rattled by the rapid spread of the virus. The Dow Jones Industrial Average sank more than 400 points, or nearly 1.5%, in early trading Monday.

Ex-Medtronic CEO Bill George told "Squawk on the Street" that he expects the outbreak to be "rough" for the next few months as China fights to contain the virus.

Stoffels also said the speed at which the virus is spreading is "scary" but doesn't constitute panic.

"But at the same time, I'm very worried that this could become a global pandemic," he said. "That's why we started working on this vaccine two weeks ago, we have to be prepared that this is going to become a global crisis."

— CNBC's Saheli Roy Choudhury and The Associated Press contributed to this report.