Marty Obst serves as Pence's senior political adviser but is not a government employee.
Marc Short, chief of staff to Vice President Mike Pence, also has been diagnosed with Covid-19, the vice president's office announced in a statement later Saturday, marking the second top Pence aide to test positive this week.
Pence spokeswoman Katie Miller tested positive for Covid-19 earlier this year.
It's not clear when Obst was last close to Pence.
The vice president, who leads the White House coronavirus task force, held a rally in Tallahassee, Florida, on Saturday evening.