Nakagawa had stepped down as finance minister after the incident at a G7 news conference, where he appeared very drowsy. He said that he had been suffering the effects of taking cold medicine.
The event hurt the credibility of the Liberal Democrat Party (LDP) government, that lost power in elections at the end of August.
Nakagawa also lost his seat in parliament during the polls.
He had entered politics at the age of 30, after the death of his father, a powerful figure in the LDP.
A forthright conservative, Nakagawa had been seen as a potential prime ministerial candidate at one time, and had held various cabinet positions, including agriculture minister and trade minister.