The shooting happened at about 12:40 p.m. Tuesday on the city's southeast side.
Capt. Jeff Hertel said a 19-year-old man contacted authorities saying he couldn't "take it anymore" and not to "send anyone because everyone will ... die."
Hertel said the man opened the apartment door and spoke with officers before running inside. The officers entered the apartment, and the man came downstairs with a "very realistic-looking" black gun.
Hertel said the man refused to drop the weapon, and the officers retreated to a bathroom before one of them shot him twice.
The captain said the officer is on paid leave during an investigation.