The debate in Salt Lake City is the first and only meeting of the two vice-presidential candidates.
The Trump-Pence camp opposed the plan, Politico reported.
"If Senator Harris wants to use a fortress around herself, have at it," Pence spokeswoman Katie Miller said.
It's not the first time plexiglass will be used in a debate as a virus precaution.
Democrat Jaime Harrison used a plexiglass partition during his debate on Sunday against Republican Senator Lindsey Graham in South Carolina.
Some Democrats are concerned that Trump may have been contagious during his debate with former Vice-President Joe Biden last week.
The Democratic nominee has so far tested negative for the virus.
Plans for a second debate are in question and the development had already informed changes to the vice-presidential debate.
Pence and Harris will stand 3.6m apart, rather than the 2m originally planned.
Biden said he is glad Trump appears to have made a swift recovery from the coronavirus, but he notes that "our nation's current crisis is far from over."
The Democratic presidential nominee made the comment in Miami's Little Havana neighbourhood while campaigning in Florida.
Trump tweeted earlier that he was leaving Walter Reed National Military Medical Centre after a three-day stay for the coronavirus.
Biden said: "I was glad to see the president speaking and recording videos over the weekend. Now that he's busy tweeting campaign messages, I would him to do this: Listen to the scientists."
He also urged Trump to support a nationwide mask mandate in federal buildings, saying he himself backed it months ago.
Biden says he's willing to go forward with an in-person debate later this month "if scientists say it's safe".
He declined to say whether he believes the next presidential debate, scheduled for October 16, should be virtual.
Instead, he said he would "listen to the science" and that "if scientists say that it's safe, that distances are safe, then I think that's fine."
Biden and Trump stood about 3m apart during the last debate, though neither wore a mask during the event. Trump tested positive for the virus just two days later.
- AP
