At least two people were taken into custody and are being questioned by police.
Birmingham Police Chief Annetta Nunn says gunfire erupted shortly after the officers arrived at the single-story dwelling converted into apartments in a low-income neighborhood.
"This is something that seems unimaginable," says Nunn.
Four officers had gone to the house to arrest Nathaniel Lauell Woods, 27, on a misdemeanor domestic assault warrant. The fourth officer was not hurt.
Nunn says police believe someone other than Woods apparently fired the fatal shots.
Kerry Marquise Spencer, 24, and Woods were booked into the Birmingham City Jail at 10:30 p.m. on suspicion of capital murder, according to early reports by the Birmingham News. Formal charges could come as early as Friday.
She said at least one more person is also being questioned but declined to elaborate. Earlier, Jefferson County Sheriff Mike Hale said five people, including Woods, had been taken into custody.
Police were consulting with prosecutors on possible charges.
Neighbors including Herman Harris said the building where the shootings occurred has a reputation as a crack house.
"They're all the time out back doing drugs," Harris said.
City spokesman Brett Oates identified the slain officers as Harley Chisholm III, 40; Charles Robert Bennett, 33; and Carlos Owen, 53, who had been on the force for 26 years. Chisholm was hired in 1998, and Bennett had been a Birmingham officer since 2001.
At least some shots appear to have been fired outside the house, in a neighborhood of modest, older homes.
One of two police cars hauled away from the scene appeared to have a window shot out, and there was glass on the street where the car had been parked.
After the shootings dozens of officers - some wearing body armor and carrying shotguns and rifles - swarmed around the house and went door-to-door in the neighborhood before the arrests were announced.
Police searched an empty lot next to the house for evidence. String they laid out to reconstruct the trajectory of the bullets indicated that at least one shot hit the Kingdom Hall of Jehovah's Witnesses building across a narrow street from the rear of the home.
The deaths marked the third time in just over a year that two or more police officers have been gunned down in Alabama.
Two police officers and a dispatcher were shot to death at the police station in Fayette on June 7, 2003. On Jan. 2, two Athens policemen were shot in an ambush after they were called to a home. A suspect has been charged with murder in each case, and each has pleaded not guilty by reason of mental disease or defect.