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 fire department spokesman told AFP, without elaborating further.
Public broadcaster NHK said a body badly damaged in the blast was found at a bicycle parking space for the park.
"The sex and ages of the three are not known yet," another local fire department official said, adding that one blast hit the facility's car park.
The Yomiuri Shimbun daily said one of the parked cars exploded and burnt down two other vehicles there.
Minutes later police found a scorched, dismembered man's body inside the park, it said.
A local festival was taking place there but was immediately called off following the blasts, it said.
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 aparts, and police found a paper believed to be a suicide note in one of the burnt cars.
The vehicle was owned by a 72-year-old former member of the Self-Defence Forces, whose house in the Utsunomiya city had been destroyed in fire shortly before the explosions hit, it said.
The man could not be reached, NHK 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.
