Andreeva was a semifinalist at last year's French Open, her best run at a major tournament.
Australian Open winner Madison Keys also reached a career-high ranking on Monday, moving up to No. 5 despite not playing a match since her triumph at Melbourne Park last month. She joins No. 3 Coco Gauff and No. 4 Jessica Pegula to give the United States a trio of women that high for the first time since 2003.
A fourth American woman, Emma Navarro, is No. 10.
Aryna Sabalenka remained at No. 1, followed by Swiatek at No. 2.
The ATP's Top 10 was mostly unchanged, with the only movement being Andrey Rublev's move from No. 10 to No. 9 after his title at the Qatar Open, swapping places with Tommy Paul.
Jannik Sinner, currently serving a three-month doping ban, stayed at No. 1, ahead of Alexander Zverev, Carlos Alcaraz, Taylor Fritz and Casper Ruud.
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AP tennis: https://apnews.com/hub/tennis