No-one was injured in the incidents and there was minimal damage to the properties, Staffordshire Police said.
The force said officers received reports of explosions at houses in the Stoke-on-Trent and Staffordshire Moorlands area on Friday night.
A spokesman said: "Shortly before 10pm last night, police were called to a house in Peters Lane, Blythe Bridge.
"A short time later another report was received at a house in Dandelion Avenue in Cheadle and just after 10.15pm a further report was received from a house in Axon Crescent, Weston Coyney."
A 44-year-old man from Cheadle was arrested on suspicion of attempted murder and is currently being interviewed by detectives.
Inspector Clare Riley, Local Policing Team Commander for Staffordshire Moorlands, said: "Incidents such as this are very rare. However, when they do happen they can have a big impact on local communities.
"Public safety is of paramount importance. I want to reassure residents in these three areas that these were targeted, malicious acts following a dispute.
"Police officers remain in the areas today to help reassure residents and I would urge residents to speak with them if they have any concerns."
Anyone with any information is asked to contact Staffordshire Police by ringing 101 or call Crimestoppers on 0800 555 111.