The inauguration is already largely virtual. Instead of in-person traditional events, there will be a prime-time television special on the night of the inauguration. From this USA Today article:
Tickets to the swearing-in ceremony are limited; parade viewing stands have been dismantled near the White House to discourage crowds; inaugural balls have been canceled; and health officials are urging people not to travel and attend.
Instead of thousands of people gathering on the National Mall for the festivities, the traditional parade down Pennsylvania Avenue will be replaced by a virtual parade that will be televised, the Presidential Inaugural Committee has announced.
The organisers have been discouraging people from going down to the ceremony physically. From the FAQs:
PIC is strongly encouraging all Americans to follow public health best practices and refrain from traveling to Washington, D.C. and instead join from home in new and innovative ways. Additional announcements will be made in the coming days and weeks about how Americans will be able to participate.
Since it's still important to preserve the tradition and customs, as the organisers of the inauguration ceremony had noted, Biden will continue to be sworn in on the steps of the Capitol. From WaPo:
“We definitely want to honor the big, broad traditions of the inaugural,” Tony Allen, the chief executive of the Inaugural Committee, said recently. “But we also want to be sensitive to the realities of the moment, have safety protocols first and foremost.”
[ ... ]
One priority, [Sen. Roy Blunt] said: to hold the swearing-in on the west side of the Capitol, where it has been held for 40 years. It is, he said, a way to send the message that despite the virus, the traditions of the day are being respected.
Lastly, it's worth noting that while it's almost impossible to ban visitors from going to D.C. on Inauguration Day, there are efforts by private entities such as Airbnb to complicate those plans. Closures of major landmarks in D.C. are also expected.