The arrests were made about two hours before President Donald Trump paid tribute to the US military during a speech at the Lincoln Memorial.
The Secret Service says one person was arrested for felony assault on a police officer and malicious burning.
The other was arrested for hindering a police investigation and resisting arrest. Neither individual was identified, AP reported.
It is not illegal to burn a US flag, but the Secret Service says the burning occurred beyond the limits of a permit issued by the National Park Service.
Two uniformed Secret Service officers suffered minor injuries while attempting to make the arrests.