The man, who has has not yet been identified, sustained life-threatening injuries, according to police.
UPDATE: The man, who has since been identified, has died.
Someone who knew the man was concerned about him and asked officials to check on him, prompting officers to respond at 1:11 p.m., according to the report from police. Officers were dispatched to the 8600 block of Oakleigh Road in Parkville, and when they arrived, the man was outside, threatening them with a knife, police said.
As police retreated to the intersection of Oakleigh and Trenleigh roads, the man continued to come at them with the knife, according to the report.
"Fearing for their lives, at least one of the officers discharged his or her service weapon; the man was struck multiple times," according to the account from police.
Officials said the man suffered what appear to be life-threatening injuries and was taken by Baltimore County Fire Department paramedics to a nearby hospital.
SWAT officers responded as a precautionary measure to ensure nobody else was inside the home on Oakleigh Road, according to police.
All officers involved in the shooting will be placed on administrative duties as the case is reviewed, which is standard procedure.