Wozniacki injured a shoulder last week in the Swedish Open but her Web site carried no mention of the injury, just a Twitter note stating: "21 today :) great to be home and celebrate with my friends and family :)."
Wozniacki's 21st birthday is Monday.
Clijsters reinjured her right ankle at the UNICEF Open in early June and is "forced to rest a few weeks," her Web site said.
Wozniacki has been No. 1 for a total of 39 weeks, including the last 21. The 39 weeks on top is tied with Amelie Mauresmo for ninth most.
Wozniacki has 9,915 rankings points with Clijsters second at 7,625. Vera Zvonareva (6,695) is third with Victoria Azarenka (6,465) in fourth and Maria Sharapova (6,141) fifth.
Li Na has 5,855 points, which is good for a No. 6 ranking. Petra Kvitova (5,437) is seventh and Francesca Schiavone (4,860) eighth. Marion Bartoli (4,230) and Samantha Stosur (3,405) complete the Top 10.
Roberta Vinci won last week's Budapest Grand Prix and went from 25th to 23rd in the rankings. Polona Hercog took the Swedish Open -- her first WTA title -- and jumped from 53rd to No. 37. The marks are career bests for Vinci and Hercog.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014