Mr Biden joins a growing number of political leaders getting the jab, including Vice-President Mike Pence and House Speaker Nancy Pelosi.
On Sunday, the roll-out began for a second vaccine, by Moderna, which was approved last week.
More than 500,000 Americans are said to have now been vaccinated.
"I'm doing this to demonstrate that people should be prepared when it's available to take the vaccine," Mr Biden said from Newark, Delaware, where he got the jab live on TV. "There's nothing to worry about."
He said the Trump administration "deserves some credit" for launching the country's vaccine programme.
Mr Biden's wife, Jill Biden, received her first dose earlier in the day, the president-elect said. Mr Biden's running mate, Vice-President-elect Kamala Harris and her husband Doug Emhoff are expected to receive their first shots next week.
The Biden team has set a goal of 100 million Covid-19 vaccinations in the US during the administration's first 100 days in the White House.
During the pandemic, the US has recorded more than 18 million cases and 319,000 deaths.