Covid-19 has "added a complexity to this that was difficult, it was a challenge," Galveston, Texas, Mayor Pro Tem Craig Brown told CNN's Anderson Cooper.
In Louisiana, the state is picking people up and taking them to hotels instead of shelters "because of Covid concerns," Mike Steele, communications director at the Governor's Office of Homeland Security, told CNN.
"We're trying to avoid congregate sheltering," Steele said.
Galveston added extra buses to transport people out, so that they could keep their distance from one another, Brown said.
Hotels are putting one person to a room to keep people separated, Brown said, and the city had ambulances "for those that needed isolation as they were being transported off the island," he said.
Some 2,000 hotel rooms were secured for Wednesday evening to help shelter people with social distancing, Louisiana Gov. John Bel Edwards said at a news conference.
The state is talking with additional hotels in case more capacity is needed.
The negative impact of Covid-19 on many people's financial situation will mean more people will be depending on public shelters or rooms instead of getting hotel rooms themselves, and "shelter demand could increase," former Federal Emergency Management Agency Administrator Brock Long told CNN.
"They can't necessarily get a hotel room, or they can't afford the gasoline and the cost of traveling hundreds of miles out of town, or out of an evacuation zone," Long said.
But at the same time, because of Covid-19 safety measures, shelters are "going to have to put smaller numbers of people in the traditional shelters that we used in the past at the local level of government," Long said, because of social distancing measures.With the National Hurricane Service warning of an "unsurvivable storm surge" from the hurricane, hotels were filling up. Some in the Baton Rouge, Louisiana, area were booked, CNN affiliate WBRZ reported. And shelters at Austin Regional Sheltering System were at capacity, the Texas city said."#HurricaneLaura evacuees, please continue traveling North and call 2-1-1 for more information about alternate shelter locations," the city tweeted.
The American Red Cross sheltered more than 5,000 people Tuesday night in Texas and Louisiana, the group said in a release, and it has sent more than 600 disaster workers to the area.
The Louisiana Department of Health urged people to keep the coronavirus in mind as they evacuate, to "wear a mask and keep distance from those outside of your family when possible," and if staying with friends and family, to "talk to them in advance about how can best protect yourself from COVID-19," the agency tweeted.
Before it was clear how big a threat the hurricane would become, Galveston "had to weigh very seriously if we wanted to go ahead and call for a mandatory evacuation," because Covid-19 made it more difficult to transport and house people safely.
But with the forecasts that were coming in, "we had to do that, because this hurricane could be devastating to this area," Brown said.
Now that Laura is a Category 4 hurricane, officials are hoping people are actually heeding the order.
"This is going to be, for that area, one of the worst storms they've seen in history," Long said.
Another problem with a disaster during the pandemic: Keeping up with testing.
"The challenge is we are going to be blind for this week," said Gov. Edwards of Louisiana, as testing is suspended because of the storm.
CNN's Devon Sayers and Leyla Santiago contributed to this report.