A man's body, badly burned in one of the blasts, was found at a bicycle parking area inside the park.
The explosions occurred at a park in Utsunomiya, some 100 kilometres (60 miles) north of Tokyo, shortly after 11:30 am (0230 GMT), a fire department spokesman said. It was not immediately clear what caused the blasts.
"One person was found dead," the spokesman told AFP, without elaborating.
Public broadcaster NHK said a man's body, badly burned in one of the blasts, was found at a bicycle parking area inside the park.
The broadcaster added two men, 64 and 58, suffered severe injuries. TV Asahi said they sustained shrapnel wounds, following the explosion inside the park.
"The sex and ages of the three are not known yet," another fire official said, adding that one blast hit the facility's car park.
The Yomiuri Shimbun daily said a parked car exploded, badly damaging two other nearby vehicles.
Minutes later police found the scorched body of the man inside the park at a bicycle parking area.
A local festival was taking place there but was immediately called off following the blasts, the paper added.
A man told NHK that he "smelled gunpowder in the area" after the explosions.
NHK said the sites of the two explosions were around 200 metres apart, and police what is believed to be a suicide note in one of the burned cars.
The vehicle was owned by a 72-year-old former member of the Self-Defence Forces, whose house in Utsunomiya had been destroyed in a fire shortly before the explosions hit, it said.
Explosions of this kind are rare in Japan, although small pipe bombs blasts linked to extreme leftists occasionally hit near US military bases.
In November last year, a homemade pipe bomb exploded at a controversial Tokyo war shrine, damaging the toilets at the facility but no one was hurt.
A South Korean man was later arrested and sentenced to four years in prison after admitting to detonating the bomb at the Yasukuni shrine, which has been targeted by activists who see it as a symbol of Japan's militaristic past.