Still, the abrupt removal of Ms. Regan — a reliably pro-Trump personality who has twice interviewed the president — came as right-wing media stars have faced growing scrutiny for commentary that played down fears about the coronavirus and suggested that the illness had been overhyped by President Trump’s critics.

Ms. Regan’s remarks, delivered on her Monday show, caused many colleagues at Fox Business and its corporate cousin Fox News to cringe. In front of a graphic reading, “Coronavirus Impeachment Scam,” she accused Democrats of creating “mass hysteria to encourage a market sell-off” and sowing fear about the virus “to demonize and destroy the president.”

Her monologue ran at the same time that the anchor Tucker Carlson, on his Fox News program, was exhorting elected officials to respond more aggressively to the virus. “People you know will get sick; some may die,” Mr. Carlson told his audience, which is significantly larger than Ms. Regan’s.

Off the air, Mr. Carlson has been urging Mr. Trump to take the threat of coronavirus more seriously. Last Saturday, Mr. Carlson drove from his residence in Florida to Mar-a-Lago, the president’s Florida resort, and spoke directly with Mr. Trump about the virus, according to a person with knowledge of their conversation.

In a memo this week, the Fox News chief executive, Suzanne Scott, and the network’s president, Jay Wallace, said that employees would predominantly work from home and that they expected programming changes “in the coming days” to accommodate a spike in audience interest in the coronavirus.