He told CNN he believed there would be a "significant reduction" in Covid-19 cases if every American wore a face covering.
Mr Biden also said he would order masks to be worn in all US government buildings.
The US has recorded 14 million cases and 275,000 deaths from Covid-19.
In the interview with CNN's Jake Tapper, Mr Biden said: "The first day I'm inaugurated to say I'm going to ask the public for 100 days to mask. Just 100 days to mask, not forever. One hundred days.
"And I think we'll see a significant reduction if we occur that, if that occurs with vaccinations and masking to drive down the numbers considerably."
Constitutional experts say a US president has no legal authority to order Americans to wear masks, but Mr Biden said during the interview he and his Vice-President Kamala Harris would set an example by donning face coverings.
The president's executive authority does cover US government property, and Mr Biden told CNN he intended to exercise such power.
"I'm going to issue a standing order that in federal buildings you have to be masked," he said.
He added: "Transportation, interstate transportation, you must be masked airplanes and busses, et cetera."
US airlines, airports and most public transit systems already require all passengers and workers to wear face coverings.
The Trump White House has rejected calls from American health experts to mandate masks in transportation as "overly restrictive".
In the CNN interview, Mr Biden also said he would retain Dr Anthony Fauci, the top US infectious disease expert, as chief medical adviser to the new administration's Covid-19 team.
The Democratic president-elect said he would be "happy" to take a vaccine in public to allay any concerns about its safety.
Three former presidents - Barack Obama, George W Bush and Bill Clinton - have said they are also prepared to be inoculated publicly to show that it is safe.
"People have lost faith in the ability of the vaccine to work," Mr Biden said, adding that "it matters what a president and the vice-president do."
Mr Biden's Vice-President-elect Kamala Harris, who joined him at the CNN interview, received some criticism from Republicans in September after she said she would not trust any vaccine approved by US public health officials during the Trump presidency.
The Pew Research Center says just 60% of Americans are currently prepared to take a coronavirus vaccine, up from 51% who said the same in September.
Mr Biden is preparing to take office as pharmaceutical giants are poised to ship millions of doses of coronavirus vaccines to the American public.
Pfizer, which says its vaccine is 95% effective in clinical trials, and Moderna, which says its jab is 94% effective, have both applied to the Food and Drug Administration to distribute their drugs in the US.
The UK on Wednesday became the first country in the world to approve the Pfizer vaccine for the coronavirus.