A rain delay of nearly seven-and-a-half hours forced organisers to push back top seed Serena's round of 16 match with qualifier Mallory Burdette and Venus's battle with Varvara Lepchenko to Friday.
Second seed Wozniacki was given a free pass to the quarterfinals when Andrea Petkovic withdrew with a calf injury just a few hours before their scheduled match.
Petkovic had admitted after her first round victory over Taylor Townsend that she was having some problems.
"I was really having trouble in Miami after the long match I had against Alja Tomjanovic," she said.
"My knee swelled up pretty big because we played three hours so I had to rest for three days and try to get it back to normal. And I’ve been having troubles with my calf because I was compensating because of the knee. So I was really scared for the past few days but now it’s calming down with the clay."
However, she tweeted that she was not quite fit enough to face Wozniacki.
"You guys, I had to pull out from my match with Caroline because of my right calf. It's been troubling me for the past days & it got worse this morning," she wrote.
"With the experience I've had with injuries in the past year, I've come to the conclusion it's better to be precautious now.
"Thank you for your understanding and I truly hope it's just a matter of days before I get better. I'll keep you updated."
Third seeded Australian Samantha Stosur went down to Canadian qualifier Eugenie Bouchard, retiring hurt with a leg complaint after losing the first set 6-1 and trailing 2-0 in the second.
Serbia's Jelena Jankovic ousted 19-year-old American Jessica Pegula in just 64 minutes 6-0 6-4 but was affected by the lengthy delays.
The former world number one was too strong for professional debutant Pegula, who won her first two matches before getting completely outclassed in straight sets.
"I wanted to take a nap, but I couldn't," Jankovic said. "We joked that if they rained it out, we have a shopping day.
"At the end of the day, I was lucky. I came out and played quite well."
Switzerland's Stefanie Voegele prevailed 3-6 6-1 6-3 over 10th seed German Julia Goerges.
Family Circle Cup results
Eugenie Bouchard (Canada) beat 3-Samantha Stosur (Australia) 6-1 2-0 (Stosur retired)
Stefanie Voegele (Switzerland) beat 10-Julia Goerges (Germany) 3-6 6-1 6-3
9-Jelena Jankovic (Serbia) beat Jessica Pegula (U.S.) 6-0 6-4
2-Caroline Wozniacki (Denmark) beat Andrea Petkovic (Germany) WO
Monterrey Open results
1-Angelique Kerber (Germany) beat Alla Kudryavtseva (Russia) 6-4 4-6 6-2
3-Maria Kirilenko (Russia) beat Jovana Jaksic (Serbia) 6-0 4-6 6-1
Lauren Davis (U.S.) beat Coco Vandeweghe (U.S.) 6-4 7-6(8)
- Sports & Recreation
- Andrea Petkovic