The Montgomery County Police Department said the incident happened just before 9 a.m. in downtown Silver Spring, north of Washington, D.C., after the officer was investigating the report of a "disorderly subject."
Other officers who arrived to provide backup found the officer wounded on the garage's top floor. He was rushed to a hospital where he later died, said Marcus Jones, the acting Montgomery County Police chief, at a news conference.
Jones identified the officer as Thomas J. Bomba, 38, a 13-year veteran of the department who was assigned to the 3rd District.
"Officer Bomba was a very dedicated officer who worked in downtown Silver Spring," Jones said. "We have typically been made aware of many different types of crimes that occur in downtown and Officer Bomba always been actively involved on patrol and addressing a lot of the concerns that have occurred in downtown Silver Spring."
The incident spawned a massive police response in Silver Spring, with aerial images showing dozens of police vehicles in the parking garage where the shooting unfolded.
Tactical teams and officers also were seen sweeping different levels of the garage. No suspects have been detained and no descriptions of possible suspects were available, Jones said.
At an earlier media briefing, Montgomery County Police Captain Thomas Jordan said, "to describe this as an all-hands-on-deck operation would be an understatement."
Jones said the case was being investigated as a homicide, but he also said there was no indication of an "ongoing" public safety threat.
He said Bomba was wearing a body camera at the time of the shooting but was not sure if it had been activated. The officer's weapon turned up at the scene but it was not clear if he returned fire, Jones told reporters.
Investigators were working with nearby businesses with surveillance cameras to see if any recorded the shooting, Jones said.
Some roads in the area were closed to traffic and students at several schools were sheltering in place earlier Monday, Fox 5 reported.
Bomba left behind a wife and two children.
The Associated Press contributed to this report.