DC Fire and EMS were dispatched at 11:05 on Tuesday morning to assist law enforcement in investigating an unknown substance, Public Information Officer Vito Maggiolo told The Independent.
Mr Obama has leased offices in the building since he left the White House in 2017. The building also contains the headquarters of the World Wildlife Fund, an environmentalist group.
A spokesperson for the US Secret Service, which also responded to the scene, said that the package was not addressed to any Secret Service protectees. Mr Obama lives with his family in the nearby Kalorama neighbourhood. It was unclear whether he was in the office at the time the package was received.
Authorities determined the substance was nonhazardous, and no one was harmed or evacuated, Mr Maggiolo said.
According to Fox News, the package was mailed from Hong Kong, with no return address. It reportedly contained baby powder.
Ms Trump and two other people were transported to a local hospital as a precaution, but suffered no negative effects. Investigators believe the substance was corn starch, according to NBC. That letter was reportedly postmarked from Boston.
Ms Trump’s husband, Donald Trump Jr, tweeted that afternoon that he was “thankful that Vanessa & my children are safe and unharmed after the incredibly scary situation that occurred this morning”.
He added: “Truly disgusting that certain individuals choose to express their opposing views with such disturbing behaviour.”
"No one deserves to be frightened this way," Mr Trump Jr's sister, Ivanka Trump, tweeted.