The ex-president, who was hospitalised with coronavirus last year, has been living at the resort in Palm Beach since he left the White House in January.
Now “a section of the club” has been “partially closed” and some workers have been quarantined, an insider told the Associated Press.
A person familiar with club operations said that it would be closed “for a short period of time” out of an abundance of caution.
The number of people quarantined, which part of the club has ben closed, or how it has affected the former president and first lady in unknown, the news organisation said.
A receptionist at Mar-a-Lago confirmed the closure to the Associated Press.
Mr Trump and Melania flew directly to Florida on 20 January before Joe Biden was sworn in as president, and the ex-president has played golf and met with political allies to discuss his future.
In an email to club members the club explained that the Beach Club and a la carte Dining Room were being temporarily closed, according to CNN’s Jake Tapper who tweeted it.
“We have undertaken all appropriate response measures in accordance with CDC guidance, including activating a thorough sanitisation and cleaning of any affected areas and club facilities, and we will continue our heightened environmental cleaning regimen,” the club said in the email.
The Associated Press contributed to this report.