Miller was pinching inside the Washington zone when the puck hopped over his stick. He turned back to play the puck when Ovechkin hit him in the numbers.
The hit drew the ire of Bruins forward Brad Marchand, and a scrum ensued while Miller remained on the ice.
The 28-year-old eventually picked himself up and made his way to the Bruins locker room, clutching his right shoulder/collarbone area.
Ovechkin, while not ejected, received a five-minute major for boarding.
The Russian star has been suspended three times in his NHL career, though only one of those was for hitting someone from behind.