Biden receives the coronavirus vaccine.

Mr. Biden, however, warned Americans that vigilance in the coming months was still necessary.

“It’s going to take time,” he said, encouraging people to continue to wear masks and socially distance. “If you don’t have to travel, don’t travel,” he said. “It’s really important.”

He thanked health care workers, calling them heroes, and ended with an awkward elbow bump with Tabe Mase, the nurse practitioner who administered to him the first course of the Pfizer-BioNTech Covid-19 vaccine. His wife, Dr. Jill Biden, received the vaccine privately, earlier in the day on Monday, according to a spokesman, and joined him at the hospital.

Since March, Mr. Biden’s team has been taking public health guidelines about social distancing and masks seriously, as President Trump and his aides have willfully disregarded them. But even Mr. Biden’s more careful circle has been infiltrated by the virus. Representative Cedric L. Richmond, Democrat of Louisiana and one of Mr. Biden’s closest advisers, tested positive for the coronavirus last week, the transition team announced.

Vice President-elect Kamala Harris is expected to receive her vaccine after Christmas, a spokeswoman said, following advice from doctors who recommended Mr. Biden and Ms. Harris stagger their first shots rather than receive them together.

Dr. Anthony S. Fauci, the government’s top infectious disease expert who will also be Mr. Biden’s chief medical adviser, will be vaccinated at 10 a.m. on Tuesday at what the National Institutes of Health is billing as a “kick off” event showcasing Moderna’s vaccine, which received emergency authorization from the Food and Drug Administration on Friday.