Olya Sharypova, 23, says Zverev tried to strangle her with a pillow in a hotel room in New York before she fled barefoot in fear of her life.
Screenshots of Whatsapp messages sent by Sharypova and shown to CNN Sport appear to suggest the alleged incident happened on August 23, 2019.
Sharypova described the incident without naming Zverev in an Instagram post Thursday but has confirmed she was referring to him in an interview with Russian outlet Championat.
The 23-year-old Zverev, who was runner-up in this year's US Open, disputes her allegations.
"I very much regret that she makes such statements because the accusations are simply not true," Zverev wrote in a statement posted across his social media platforms on Thursday.
"We had a relationship, but it ended a long time ago. Why Olga is making these accusations now, I just don't know.
"I really hope that the two of us will find a way to deal with each other again in a reasonable and respectful way."
Sharypova told CNN that she did not contact the police after the incident because she "loved this person and did not want to create problems for him."
CNN could not independently verify her allegations. The New York Police Department confirmed to CNN there were "no complaint reports on file."