World number six Rybakina, the reigning Wimbledon champion, was leading 6-4, 1-0 when Kalinina called it quits with a left thigh injury shortly after midnight in a final long-delayed by rain.
Rybakina, 23, is the first player to capture two WTA 1000 titles this season having already won the prestigious Indian Wells hard court tournament.
She was also runner-up at the Australian Open and in Miami.
“I wish Anhelina a speedy recovery, she’s a good friend of mine,” said Rybakina after the 68-minute final which only got underway at 11pm.
“She has done an amazing job, I hope she is fit for Roland Garros.”
She told the hardy fans in the stadium, who had sat through more than four hours of rain delays: “Today was not easy for players – but it was also not easy for you.”
Rybakina, who will rise to four in the world ahead of the French Open, is only the third woman to have reached the finals at the Australian Open, Indian Wells, Miami and Rome in the same season.
The others were Monica Seles in 1991 and Maria Sharapova in 2012.
The Russian-born Rybakina has now won 28 matches this season — only world number two and Australian Open champion Aryna Sabalenka has won more, with 29.
Kalinina, 26, said that her physio had kept her fit enough to compete until the end in Rome.
“I tried my best but I just could not play,” Kalinina said, apologising to spectators.