Two cars, a wheelie bin and a fence were damaged by a fire believed to have been started deliberately in the early hours of Monday morning in Wick Close, Corby.
Northamptonshire Police say they would like to speak to anyone who may have seen a man acting suspiciously around the time of the incident, which happened between 3.45 and 4am.
He was a white man, around 6ft, of medium build and was wearing a white hat, white hooded top, grey tracksuit bottoms and white trainers. He was carrying a rucksack on his back.
No-one was injured in the fire.
Witnesses or anyone with information about this incident are asked to call Northamptonshire Police on 101.
Alternatively, they can call the independent charity Crimestoppers anonymously on 0800 555 111 or use the anonymous online form at www.crimestoppers-uk.org.