The boar bit a 74-year-old man on the back and leg, knocked a 74-year-old woman to the ground and bit a 24-year-old woman on the legs before she took refuge in a parked car, police said in a statement. The three were taken to hospital.
The fourth person to be injured was a police officer who had been sent to the residential neighbourhood of Charlottenburg to investigate, after passers-by reported the presence of the boar, police said.
The animal attacked the officer and bit him in the leg before he used his police-issue gun to kill it.
Marc Franusch, spokesman for the Berlin Foresters, told the Berliner Morgenpost newspaper the boar had a broken front leg, probably sustained when hit by a car.
"It could have been scared by dogs or people out of its resting place under a hedge, and was carrying a painful injury," said Franusch. He said it was possible that the frightened animal had panicked and reacted aggressively.
There are thought to be around 4,000 wild boars in the capital, mostly living in the woods and similar areas. Such attacks are extremely rare.