The attacks came in the town of Song, near the border with Cameroon.
A policeman, a soldier, a civilian and his grandchild were killed, the Adamawa state police spokesman told the BBC.
They have often targeted Adamawa state but this is believed to be the first time Song has been attacked.
Local residents say some of those who died were burnt to death.
Police spokesman Mohammed Ibrahim told BBC Hausa that extra security forces had been sent to the area.
He said there had been no arrests.
Last week, there was a similar attack in Maiha, also in Adamawa state.