One of the football goals at Peel Park in Clanfield was set alight, causing anger to residents.
According to Hampshire Police, a report was received at 7.30pm on September 15 that the net was on fire but had been put out.
A Clanfield Parish Council spokesperson said: “The Parish Council is shocked and saddened by this incident.”
The goal belongs to the Clanfield Football Club and there is concern about the cost and finding a new replacement. The lack of a goal means upcoming games could be cancelled, which would affect the children of the village.
Anyone with information should call 101, quoting reference 44240396795 or make a report online.