There were more than 20 aboard the ship who tested positive for novel coronavirus in limited early testing as of this weekend.
"The vice president met with the CEOs of the major cruise ship companies yesterday, and they are coming up with a plan within 72 hours of that meeting," Carson told ABC News Chief Anchor George Stephanopoulos on Sunday.
When Stephanopoulos pressed, noting that the cruise ship will dock in California on Monday, less than 72 hours from Pence's meeting, Carson said, "The plan will be in place by that time."
In more than 100 countries, at least 106,000 people have been infected with COVID-19 and more than 3,594 people have died, according to numbers released by Johns Hopkins University Sunday morning. In the U.S., at least 433 cases of the coronavirus have been reported in 31 states and Washington, D.C., and 19 people have died.
The Italian prime minister recently announced travel restrictions in the Lombardy region of northern Italy which would limit movement in, out and around the region through April 3.
New York, where there have been 76 cases of novel coronavirus, declared a state of emergency on Saturday and public events around the world have been canceled.
On "This Week" Sunday, Stephanopoulos asked if communities should take more extensive measures to respond to the coronavirus, but Carson focused on steps that individuals could take.
"I think it’s time for people to really indulge themselves in learning about how viruses are spread. And to take advantage of that knowledge in determining what their daily activities are going to be," he said, adding that people in high-risk categories should avoid attending rallies and large crowds.
When Stephanopoulos pressed Carson on the broader measures that could be taken, the HUD secretary said those recommendations would come from the Centers for Disease Control and Prevention.
In a separate panel on "This Week," Tom Bossert, a former Trump homeland security adviser who worked on bio preparedness, said he was "very disappointed" to hear that messaging from Carson.
While he gave credit to the Trump administration for working quickly to contain the virus, he said, "it’s not about individual prevention. That’s important, and the doctor will tell you that, but as a collective public we need to start mobilizing this collective risk mentality."
Vice President Mike Pence said Saturday that doctors can prescribe the coronavirus test to any American, regardless of symptoms. The CDC changed its guidance on Tuesday, which had previously limited testing to people who had traveled in regions affected by the outbreak.
"At the present moment we've distributed more than 1 million tests, and in cooperation with those same commercial labs that I mentioned, we'll be expanding access to tests in the weeks ahead to every American," Pence said.
Carson said Sunday on "This Week" that another 640,000 tests would be available Monday.
President Donald Trump signed an emergency funding bill that allocates $3.8 million to combat novel coronavirus Friday.
ABC News' Ahmad Hemingway contributed to this report.