Two bottles containing lit rags were thrown at a house in Wolverton in the early hours of Monday morning.
Police are appealing for witnesses to the incident which took place in Green Lane at around 4am.
The bottles hit the wall of the property but did not cause any significant damage.
Investigating officer Det Con James Shepherd from Milton Keynes Force CID said: “Although there was little damage to the property, we are taking this very seriously.
“I want to reassure the community that we are investigating this incident thoroughly and officers are patrolling the area today, conducting house-to-house enquiries.
“I urge anyone with information to get in touch immediately.”
Anyone with information can contact Det Con Shepherd via the 24-hour Police Enquiry Centre on 101.