Caprioriu was penalised for trying to hold Matsumoto's leg to flip over the Japanese.
Defeated semi-finalist Marti Malloy won the bronze medal after defeating defending Olympic champion Giulia Quintavalle from Italy.
USA's Malloy sealed the fate of the match within a short span of time by pinning Quintavalle on her back to score an Ippon.
The second bronze medal was bagged by Automne Pavia from France after she defeated Hedvig Karakas by a swift leg sweep which resulted in the Hungarian's fall.
Pavia climbed down to hug her coach before greeting French President Francois Hollande.
Matsumoto dedicated Japan's first Judo gold of the Games to her team-mates Tomoko Fukumi and Misato Nakamura.
She said: 'I am so very happy to be able to get gold on behalf of my colleagues.
'There was pressure, but I did what I wanted to do along the way which helped me to win the medal.
'I had a strong feeling to win, told myself to calm down, focus and not to give up.
'Fukumi had told me to go for it and Nakamura that I would get the first gold medal for Japan.'