As Mr Pence was receiving his jab, Mr Trump incorrectly said on Twitter that the Moderna vaccine was "overwhelmingly approved" with "distribution to start immediately". It is still awaiting final approval from the Food and Drug Administration (FDA).
More than 310,000 people have died with coronavirus in the US, which has recorded more infections and fatalities than any other country. More than 17 million cases have been recorded in the country since the start of the pandemic.
Mr Pence, 61, received the first of two doses of the Pfizer/BioNTech jab at 08:00 local time (13:00 GMT), along with his wife Karen and Mr Adams. He is the most senior US official to be vaccinated so far.
"We gather here today at the end of a historic week to affirm to the American people that hope is on the way," he told the crowd, after the number of newly-recorded US coronavirus deaths surpassed 3,000 for the third day in a row.
"Karen and I were more than happy to step forward before this week was out to take this safe and effective coronavirus vaccine that we have secured and produced for the American people," he continued, calling it "a truly inspiring day".
Top infectious diseases expert Dr Anthony Fauci, and Centers for Disease Control and Prevention Director Robert Redfield were in the audience to observe the doctors from Walter Reed hospital perform the injections.
Both men elbow-bumped Mr Pence and his wife after their jabs. Mr Trump did not attend the event.