Pence, meanwhile, successfully received the vaccine alongside his wife Karen and Surgeon General Jerome Adams during a televised White House event in the Eisenhower Executive Office Building on Wednesday.
"Hope is on the way", Pence said.
Former Presidents Bill Clinton, George W. Bush, and Barack Obama have said they will take the vaccine publicly as well to inspire confidence among Americans.
His wife Karen Pence and prominent USA public health officials and general surgeon Jerome Adams were also vaccinated with the Pfizer-BioNotech vaccine at the White House pavilion.
"The American people can be confident: We have one, and perhaps within hours, two safe vaccines", he added with an apparent nod to Moderna's forthcoming COVID-19 vaccination, which is awaiting FDA authorization.
Biden and incoming first lady Jill Biden are set to receive the first dose of Pfizer's coronavirus vaccine Monday.
Signalling the importance given to the event, top infectious diseases Anthony Fauci and Centers for Disease Control and Prevention director Robert Redfield were also in the room.
Trump will not be administered a coronavirus vaccine until it's recommended by the White House medical team, a White House official told CNN earlier this week.
Even as high profile figures like US Vice President Mike Pence rolled up their sleeves for Covid-19 vaccinations, patients already ill with the disease crowded emergency rooms and overran intensive care units in California, now a worldwide epicenter.
"I think at this point, whoever can get it, should get it", says Chris Auer, of Bethpage.
He sat on a chair while he took the vaccine.
"He will be doing it in public, which is important to us, as he's stated many times, to send a clear message to the public that it's safe", Biden spokeswoman Jen Psaki told reporters. White House officials have described it as a hard position: They are torn between wanting to instill public confidence in the vaccine by taking it and not wanting to be seen as jumping the line, given the limited supply.