Masked health professionals check the driver of vehicle at a screening checkpoint on a highway toll station on the outskirts of Shanghai, China, on Tuesday, Jan. 28, 2020.

"I'm not one to take offense very easily so I wasn't angry, just kind of chuckling under my breath like 'wow, this is really happening'." Han said he did not report the driver to Uber. Weeks earlier, Han said he was told by a group of strangers in downtown Seattle to "go back to my homeland."

The driver commented that his cough meant he might have the coronavirus, and opened a window.

Eric Han, who works in a Microsoft retail store in Seattle, told CNBC he called an Uber on Monday, stepped into the car and coughed. It was a cold day. His driver immediately asked if Han was from China, and he responded that he was not.

A CNBC search found dozens of tweets involving riders and drivers reluctant to share a car with a person of Asian appearance. Many of these tweets were posted in the past week, as fears have been stoked by reports that there are now confirmed cases of the virus in more than half a dozen countries.

For ride-sharing platforms Lyft and Uber , these incidents appear to be happening despite their efforts to curb discriminatory behavior. One member of a Facebook group with more than 12,000 Lyft and Uber drivers noted that at least five posts per day mention the virus. The member, who shared screenshots with CNBC, said that many drivers were saying they did not want to pick up riders of Asian descent and that it was not safe to do so.

Han is far from alone. When Lilian Wang attempted to get into her Lyft ride share at San Francisco airport on Sunday, a driver refused to open the car door.

According to Wang, who is Asian American and works in the technology sector, the driver let them in only after a Caucasian friend showed up — CNBC video producer Katie Schoolov, who says she put in the request for the ride.

Once in the backseat, the driver asked if the pair were returning from China and Schoolov responded that they'd just returned from Mexico. "OK, so not China," he responded.

Their driver then noted that he's been told to be careful and has refused ride requests from people with Chinese-sounding names. He also asked Wang if she was in fact, a rider called "He," and noted that he had already turned down that request.

After registering a complaint, Schoolov received a call from a representative from Lyft's support team informing her that the driver had been removed from the platform.

On Saturday in Chicago, Indra Andreshak said she took a shared ride in a Lyft and the driver was alerted to two other riders who needed a pickup nearby. The app pulled up a profile picture of the first passenger, who Andreshak noted was "visibly Asian and named Hero." She then said she heard her driver say "Hero, Heee-ro, Hero in Chinatown."

"I hope he doesn't give me the coronavirus," the driver muttered. Andreshak said she reported the incident.

Myeonghoon Han said five days ago in London he called an Uber with some Korean friends. They piled in and the driver looked annoyed and waved his hands, indicating he did not want them in the car. Han said his friend said "we're not Chinese," and the driver's demeanor changed drastically and he was happy to drive them to their destination. The group did not report the incident.

Lyft spokesperson Dana Davis said in a statement that the company takes "any allegation of discrimination very seriously." Davis added that Lyft is "monitoring official updates on the global outbreak closely, and taking our cues from international and domestic public health experts."

"Our priority is to keep our riders, drivers and employees safe, with as little disruption as possible. We will continue to evaluate the situation as it unfolds, and base our policies and recommendations on official guidance," she said.

Lyft did not respond to CNBC about whether the company would be rolling out any broader policies to combat discrimination, including public health resources and education. Instead, they are asking riders to share their experiences with their safety team.

Uber referred CNBC to its community guidelines that drivers are required to acknowledge. Those guidelines specify that drivers should "foster positive interactions" with people who "might not look like you or share your beliefs." It also said it has a portal for public health authorities, and that it is in regular contact with these groups.

In Mexico City, Uber confirmed on Saturday that it suspended the accounts of 240 users who may have recently come into contact with the coronavirus.

China's National Health Commission confirmed on Monday that there have been 361 deaths from the virus. So far, there have been 11 confirmed cases in the U.S., out of more than 17,000 total. Public health officials say the flu is a higher threat in the U.S., and has led to 10,000 deaths during the influenza season.