None of the companies represented immediately responded to a CNN request for comment.
The person's identity was not immediately clear, but a source familiar with the event's planning said she was there on behalf of the administration.
A source familiar with the situation told CNN that employees went out and "politely informed everyone that because they were six feet apart, that if they wanted, they could remove the mask."
"She did not ask, and she did not ask them to remove their masks," the source said, noting that the CDC guidelines say masks are not necessary if it is possible to maintain six feet of social distance.
A few minutes later, Pence showed up to begin the roundtable, which focused on outbreaks at meat processing plants and security concerns in grocery stores.
A White House official told CNN that the vice president's advance staff "takes precautions to keep participants around the table at least six feet away – meaning you don't have to wear a mask based on CDC guidance – so they can't have wear masks and have a more engaging dialogue. "
"Participants, who have taken their positions and are shown by doctors, are always more than welcome to do whatever they want," said the official.
The White House has said that anyone who comes near Pence or President Donald Trump is administered a coronavirus test, and people who enter the White House undergo temperature screening.
But mask wear has been rare among White House staff – a fact drawn after two West Wing employees tested positive for the virus last week.
However, Trump has not been photographed wearing a mask and has said he can't imagine wearing one in the White House. While visiting a mask manufacturing facility in Arizona last week, he briefly had one scene, but people familiar with the matter said he seemed uncomfortable and was told by factory management that there was no need to wear one.
Last month, the White House updated its recommendations on wearing masks, suggesting that Americans cover their faces when social distancing is difficult.
In the White House, masks have been a rare sight among employees, who often take the president's lead in their messages and behavior.
Chief of Staff Mark Meadows told reporters last week that people serving the president would start wearing masks.
Trump administration officials spent the weekend trying to make contact with Katie Miller, Pence's press secretary who tested positive for coronavirus last week.
But they had not identified who Miller infected the virus with as of Sunday, and raised concerns inside the White House about how to contain the outbreak.
Iova's Republican Prime Minister Kim Reynolds, who attended Pence's roundtable on Friday and also visited the White House last week, announced Monday that she is following a modified quarantine protocol for coronavirus out of concern that she may have been exposed to the virus during the trip . Reynolds said she did not have direct contact with Pence staff, but said she would follow a modified quarantine based on an abundance of caution.
Some helpers expressed concern about how Monday would go without much clarity in how the virus had spread and spread. An official said it was not certain which colleagues would be at home. Some officials who had extended contact with Miller announced that they would quarantine themselves, while others who had similar contact with her did not.
In conversations over the weekend, Trump has expressed concern that helpers who infected the virus would undermine his message that the outbreak is declining and that states should start reopening, according to a person who spoke to him.
Trump expressed frustration that two White House staff tested positive for coronavirus and have asked why his officers were not ordered to wear masks until this week, according to the person.
Trump believes an economic rebound will only come when governors decide to lift the restrictions and are worried about any signs of the virus emerging.
At the same time, he told people he will not be near anyone who has not been tested and busted when they came in contact with some people in the White House.
Pence does not plan to go into the self-quarantine and arrived at the White House on Monday morning without wearing a mask.