Wozniacki tweeted Saturday that fans made threatening comments to her family, including her parents, and cursed at the niece and nephew of her fiancé, David Lee.
"I am fully aware that tennis is a game of wins and losses. However, during the match last night people in the crowd threatened my family, wished death upon my mom and dad, called me names that I can't repeat here and told my Fiancé's niece and nephew (who are 10 years old) to sit down and shut the f--- up," Wozniacki wrote. "Meanwhile security and staff did nothing to prevent this and even accepted this to take place. While I always encourage fans to cheer for their favorite player, and I thrive on a challenging atmosphere, when certain lines are crossed, it makes tennis miserable for both competitors."
Wozniacki called on Miami Open organizers to take the incident seriously.
Lee, who played for five teams over a 12-year NBA career, also tweeted Saturday, calling it a "disgusting atmosphere" in Miami.
Disgusting atmosphere, hope something can be done to prevent this from happening again! https://t.co/fi1mcRqLcw
— David Lee (@Dlee042) March 24, 2018
Tournament director James Blake said in a statement that tournament and WTA staff, as well as security, did not see or hear any specific threats.
"The security of the players is our No. 1 priority," Blake said. "Last night's match between Caroline and Monica was played in front of a loud and passionate crowd. While I personally feel that no one should have to endure any sort of abuse on the court, we do our best to provide a safe and fair environment."
Blake added that they would have handled any issues immediately if they had been notified of them. Wozniacki complained to the chair umpire during the match about crowd noise, but Blake said the tournament was unaware of any threatening comments.
The No. 2 seed in Miami, Wozniacki was upset 0-6, 6-4, 6-4 by Puig, who will face Maria Sakkari in the third round.
Puig is from Puerto Rico and is especially popular in South Florida, while Wozniacki is from Denmark.
The Associated Press contributed to this report.