Mr Biden’s spokeswoman said now was not the time to be easing travel measures.
Security is intense in Washington DC ahead of the inauguration ceremony.
Thousands of National Guard reserve soldiers have been deployed in the wake of the storming of the Capitol building by a pro-Trump mob on 6 January that left five people dead.
The FBI had earlier warned of possible protests across the nation by right-wing extremists emboldened by the invasion.
What was the Trump decree about?
The US imposed travel restrictions on Europe last March and the Brazilian entry ban was put in place in May, but the White House decreed on Monday that the entry ban would end on 26 January, six days after Mr Biden takes office.
Just minutes later, Mr Biden’s spokeswoman, Jen Psaki, said on Twitter: “On the advice of our medical team, the administration does not intend to lift these restrictions on 1/26. In fact, we plan to strengthen public health measures around international travel in order to further mitigate the spread of Covid-19.”
She said that with “more contagious variants emerging around the world, this is not the time to be lifting restrictions on international travel”.
What else might Trump do on his final full day?
Barred from Twitter following the Capitol riots, the president has been uncharacteristically quiet and there have been few details of what he might do on Tuesday.
A statement from the White House press office read simply: “President Trump will work from early in the morning until late in the evening. He will make many calls and have many meetings.”
There has been no invitation to Joe Biden for the traditional pre-inauguration meeting at the White House.
Mr Trump still contests the election he fought with Mr Biden, although he has pledged a transition of power.
The main focus will be on presidential pardons, with US media suggesting a list of some 100 people is being considered.
The New York Times said some could be of criminals whose cases have been championed by justice activists.
More controversial names include Edward Snowden, Julian Assange and Mr Trump’s former adviser Stephen Bannon.
Rapper Lil Wayne, a prominent Trump supporter, is also reported to be on the list.
He pleaded guilty to possession of a gold-plated handgun, which was loaded when his chartered private jet landed in Miami in December 2019.
Friends of Joe Exotic, the star of the Netflix documentary Tiger King who is serving a 22-year sentence for his involvement in a murder-for-hire plot and animal abuse, are also hopeful he could be pardoned.
Then, of course, there is Donald Trump. Could the president pardon himself? It is unclear either whether he plans to do so or even if it is legally possible.
What of the inauguration ceremony?
The ceremony will be unlike any other. The number of spectators will be greatly reduced, some 25,000 National Guard soldiers are being deployed and Donald Trump will snub his successor by not attending – something that has not happened for more than 150 years.
On Monday, the Capitol complex was briefly locked down after a security alert.
Some 200,000 flags, bathed in light, have been planted on the National Mall to represent the crowds who cannot attend and reflect on those who have lost their lives to Covid.
The inauguration ceremony will feature performances by Lady Gaga and Jennifer Lopez.
Mr Trump will head to Florida early on Wednesday, using up his presidential travel privileges by taking Marine One to Joint Base Andrews and then boarding Air Force One.
Bloomberg said Mr Trump was planning a military send-off for himself at Andrews.
What is Joe Biden initially planning to do?
On Tuesday he is scheduled to deliver an evening address on Covid from the Lincoln Memorial in Washington DC.
He is set to immediately reverse a number of Trump policies, scrapping the ban on travellers from some mainly Muslim countries and rejoining the Paris climate accord.
He will also focus on reuniting families separated at the US-Mexico border and issuing mandates on Covid-19 and mask-wearing.
Mr Biden will also cancel the controversial Keystone XL Pipeline on his first day in office, US media report.
The pipeline is projected to carry oil nearly 1,200 miles (1,900km) from the Canadian province of Alberta down to Nebraska, to join an existing pipeline. Environmentalists and Native American groups have fought the project for more than a decade.
Confirmation hearings for Mr Biden’s appointees begin later on Tuesday.