Eastbourne, where Rybakina was seeded No.1, made the announcement before the Kazakh star's scheduled first-round match on Monday.
Moscow-born Rybakina made her major breakthrough by winning the title at Wimbledon last year and has steadily gone up the world rankings in 2023.
She was among the favourites for the French Open but pulled out of Roland Garros ahead of her third-round meeting with Sara Sorribes Tormo earlier this month, also due to a viral illness.
Rybakina, who also lost to Donna Vekic in the round of 16 in Berlin last week, said: "Unfortunately, I have to withdraw here in Eastbourne today.
"I am still recovering from the virus I had in Paris and after Roland Garros it was really tough.
"I also picked up another small issue in Berlin, so my team and I decided it would be better to recover this week and prepare for Wimbledon."
Also at Eastbourne on Monday, Russian Daria Kasatkina branded the war in Ukraine "s***" following her first match in Britain for two years and revealed she is "very worried" about loved ones back home.
World No.11 Kasatkina, who was banned from competing in the UK last year due to the ongoing conflict, overcame Ukrainian Anhelina Kalinina 6-3 6-1 in a politically-tense first-round match.
The 26-year-old has been following the news on a daily basis since the outbreak of war and feared friends living in the Russian city of Voronezh could be caught up in the recent rebellion by the Wagner mercenary group.
Kasatkina, who is now based in Dubai, acknowledges Ukrainians are in a "way worse situation" and concedes she cannot see an imminent end to the fighting.
"My family, my parents are still in Russia," she said. "As you can see, the last few days it's been a big mess also there.
"I'm worried for my friends, because my best friends they actually live in Voronezh, where the guy with the private army (Yevgeny Prigozhin, leader of Wagner) entered.
"I was pretty worried about that because they were very scared.
"Obviously Ukrainians, they are experiencing a way worse situation but also I can feel the same. I'm very worried for the people I love.
"It's been a tough year, and we don't know how long it's going to be. Honestly, so far I don't see the end.
"(It) feels s***, honestly. I'm not gonna hide it. It's tough to face the circumstances for such a long time already. I'm just trying to be a good human in this scenario. That's all I can do."
Kasatkina was booed off court earlier this month following her defeat by Ukraine's Elina Svitolina at the French Open.
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