The world number six led 6–4, 1–0 when final opponent Anhelina Kalinina of Ukraine was forced to throw in the towel due to injury.
"I hope you recover to the French Open," Rybakina said in her victory speech.
"Secondly, I would like to say a big thank you to the audience who stayed and watched until the end. It was not easy for us, but it was also not easy for you with all the delays due to the rain, so thank you for all the support.
The 23-year-old Rybakina is the first player to secure two WTA 1,000 titles this season after securing victory in prestigious Indian Wells earlier this year. She also finished second at the Australian Open. With the victory, Rybakina will climb to fourth place in the world rankings for the French Open.
She is also the third woman to reach the final of the Australian Open, Indian Wells, Miami and Rome in the same season, something only Monica Seles and Maria Sharapova have previously achieved, in 1991 and 2012 respectively.