Its report suggests the hardest-hit sections of the population are black men, and people aged between 40 and 49.
The infection rate puts Washington DC on a par with Uganda.
But one factor may be a drive towards more HIV/Aids testing, and the city government insists much is now being done to tackle the problem.
According to the report, both the United Nations and the US Centers for Disease Control and Prevention (CDC) have "historically defined an HIV epidemic as generalised and severe when the overall percentage of disease among residents of a specific geographic area exceeds 1%.
"The overall proportion in the District is three times higher," the report says. By comparison, less than half of 1% of Americans are living with cancer.
Even the 3% figure, the report says, is certain to be an underestimate, as so many of Washington's residents are unaware that they are infected.
"In the District, nearly every population group and age is experiencing a substantial epidemic," the report says, with the greatest rates of infection among black men (6.5%), Hispanic men (3.0%), and white men (2.6%).
In terms of age, those aged 40-49 are the worst affected (7.2%), followed by those aged 50-59 (5.2%).
The main mode of transmission is men having sex with men, followed by heterosexual sex and infection through drug use.
'Actually 5%'
The chief medical officer at the Whitman-Walker clinic, one of Washington's biggest HIV organisations, told the BBC that the real figure could be even higher.
"When they've tested large groups of the District population it looks like the prevalence is actually about 5%, which is higher than the 3% but a lot of the people haven't been tested yet," said Dr Raymond Martins.
"I think we're seeing the increase recently because the new director of our HIV/Aids administration here in Washington has put a large push for everyone to get tested and so with that testing you're discovering all these people that are HIV-positive that didn't realise they were."
The report says the city's Mayor Adrian Fenty and the department are following a three-pronged strategy to tackle the epidemic, by promoting testing for the virus, preventing transmission by providing free condoms and needle exchanges, and doing more for those already living with HIV/Aids.
