The agents, assigned to protect Naomi Biden, were out with her in the Georgetown neighbourhood late on Sunday (Monday AEDT) when they saw the three people breaking a window of the parked and unoccupied SUV, the official said.
The official could not discuss details of the investigation publicly and spoke to the AP on Monday on the condition of anonymity.
One of the agents opened fire, but no one was struck by the gunfire, the Secret Service said in a statement.
The three people were seen fleeing in a red car, and the Secret Service said it put out a regional bulletin to Metropolitan Police to be on the lookout for it.
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Washington has seen a significant rise in the number of carjackings and car thefts this year. Police have reported more than 750 carjackings this year and more than 6000 reports of stolen vehicles in the district.
US Representative Henry Cuellar of Texas was carjacked near the Capitol last month by three armed assailants, who stole his car but didn’t physically harm him.
Violent crime in Washington has also been on the rise this year, up more than 40 per cent compared with last year.
In February, US Representative Angie Craig of Minnesota was assaulted in her apartment building, suffering bruises while escaping serious injury.