Mr Nakagawa, 56, was found dead in a bedroom at his Tokyo home, Japanese news agencies reported.
The long-time LDP lawmaker stepped down as finance minister after appearing groggy at a news conference in February at G7 talks in Rome.
He then lost his seat in his party’s 30 August election drubbing.
The cause of Mr Nakagawa’s death was under investigation, a police spokeswoman told the Associated Press news agency.
Japanese media reports said he was found face down on the bed by his wife, with no external injuries.
The incident at the Rome summit was a major embarrassment for the Japanese government, says the BBC’s Roland Buerk in Tokyo.
Mr Nakagawa later denied he had been drunk, blaming jet lag and medicine he had taken for a cold.
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