Matsumoto, 24, the world number one, who had been fast, aggressive and determined throughout the tournament, won the final after Corina Caprioriu of Romania was penalised for a leg grab.
Japan traditionally dominates judo at the Olympics but this was the first medal won by one of the team's women.
Earlier, she had beaten Italian Giulia Quintavalle, the reigning champion, in the quarter-final before overcoming France's Automne Pavia in the semis.
Caprioriu, the 26-year-old sixth seed, reached the final by beating American Marti Malloy in the last four with an automatic winning ippon, throwing her to the tatami (mat) with just seconds left.
Malloy, who put out the number two seed Telma Monteiro in the first round, overcame Quintavalle to win bronze. Clearly overwhelmed the 26-year-old American from Washington State shed tears as she pumped the air with her fists in joy.
France's Automne Pavia, 23, who was impressive in her first Olympic Games, took the other bronze by defeating Hungary's Hedvig Karakas, in front of her country's president, following on from Priscilla Gneto who won bronze for France on Sunday.
A delighted Hollande personally congratulated her to cheers from the large contingent of French fans in the crowd.