The announcement on Wednesday sets up duelling town halls with Democratic opponent Joe Biden on a night the two candidates were supposed to meet for their second debate.
Mr Biden is appearing on a similar town hall event in Philadelphia, televised by ABC.
NBC said Mr Trump would be at least 12 feet from moderator Savannah Guthrie and the audience.
Mr Trump, who tested positive for Covid-19 on October 2 and spent three days at the Walter Reed military hospital, took a coronavirus test administered by the National Institutes of Health, NBC said.
Both NIH clinical director Dr Clifford Lane and Dr Fauci reviewed Mr Trump’s medical records and said they had a high degree of confidence that the president is “not shedding infectious virus”.
Mr Trump’s ability to reach a national television audience on Thursday was in part dependent on Dr Fauci, who had expressed anger at the Trump campaign in recent days for using one of his statements in a campaign ad.
The coronavirus task force member said a quote used in the campaign ad was taken out of context.
A formal match-up between the Republican president and Mr Biden that was scheduled for Thursday in Miami by the non-partisan Commission on Presidential Debate was cancelled.
In light of the president’s infection, the commission shifted the format to a virtual meeting, and Mr Trump declined to participate.
Both town halls will begin at 8pm Eastern, but Mr Biden will have the last word.
I’ll be a president for all Americans. Not just the ones who vote for me.
Advertisement— Joe Biden (@JoeBiden) October 14, 2020
The ABC event, moderated by George Stephanopoulos, will last 90 minutes with an additional half hour of analysis.
Mr Trump’s town hall on NBC is scheduled for an hour.
In addition to preventing viewers from getting a side-by-side comparison of the two men, the duelling events will likely be seen by far fewer people.
The first debate between the two men last month was watched by an estimated 73.1 million people, the Nielsen company said.
An estimated 6.7 million people saw Mr Biden at an NBC News-sponsored town hall last week.
Like the Trump event on Thursday will be, it was simulcast on MSNBC, CNBC and streamed online.
Mr Trump’s town hall with Mr Stephanopoulos on September 15 was seen by 3.8 million people, Nielsen said.
Thursday’s Trump town hall on NBC will be held outdoors at the Perez Art Museum in Miami.
Audience members will be socially distanced, required to wear a mask and submit to a temperature check before entering the venue, NBC said.
