Rybakina, who came into the match as the only woman left in a decimated draw to have lifted the Venus Rosewater Dish, found herself an early break down but the 2022 champion settled her nerves quickly.
The Moscow-born Kazakh broke back before drawing level at 3-3 when Kalinskaya began to struggle with a right forearm issue that she had treated after losing another game.
Anna Kalinskaya has her arm attended to by a physio during her match against Elena Rybakina. (EPA PHOTO)
Kalinskaya appeared to have overcome the problem, much to the relief of her boyfriend and world No.1 Jannik Sinner, who was watching on from the Centre Court stands, but she was unable to prevent Rybakina from winning the first set.
The 25-year-old saved a breakpoint with a powerful ace and consolidated a break in the second set for a 2-0 lead, but the problems returned for Kalinskaya.
She dropped another game to go a double break down before throwing in the towel and walking off disappointed.
Ukrainian Elina Svitolina fought back tears after her 6-2 6-1 victory over Wang Xinyu  following news of a Russian missile attack in her home country
"It's a very difficult day today for Ukrainian people," she said. "So yes, it was not easy to focus today on the match. Since the morning, it's very difficult to read the news."
A major Russian missile attack across Ukraine killed dozens and injured more than 150 people, officials said. One missile hit a large children's hospital in the capital of Kyiv.
Svitolina, who has reached the semi-finals twice at the All England Club, including last year, wore a black ribbon on her white shirt during the match. "Thank you for your support," she told the Wimbledon crowd
