US showbiz website TMZ said Yolanda Hadid, 57, has accused the former One Direction singer of an alleged assault last week.
Zayn, who has one-year-old daughter Khai with model Gigi, 26, issued a denial to TMZ, while People magazine reported the couple had split.
He told the outlet: “I adamantly deny striking Yolanda Hadid and for the sake of my daughter I decline to give any further details and I hope that Yolanda will reconsider her false allegations and move towards healing these family issues in private.”
In a separate post on social media, 28-year-old Zayn referenced the allegations and asked for privacy.
He said: “As you all know I am a private person and I very much want to create a safe and private place for my daughter to grow up in.
“A place where private family matters aren’t thrown on the world stage for all to poke and pick apart.
“In an effort to protect that space for her, I agreed to not contest claims arising from an argument I had with a family member of my partner’s who entered our home while my partner was away several weeks ago.”
Seemingly hinting that he and Gigi had split, Zayn added he wants to “co-parent my daughter in a manner in which she deserves”.
He said: “This was and still should be a private matter but it seems for now there is divisiveness and despite my efforts to restore us to a peaceful family environment that will allow for me to co-parent my daughter in a manner in which she deserves, this has been ‘leaked’ to the press.
“I am hopeful though for healing for all involved with the harsh words shared and more importantly I remain vigilant to protect Khai and give her the privacy she deserves.”
A representative for US catwalk star Gigi, who has been dating the Bradford-born singer on-and-off since 2015, also asked for privacy.
In a statement to E! News, the representative said: “Gigi is solely focused on the best for Khai. She asks for privacy during this time.”
Yolanda, a Dutch-American television personality and former model best known as a star of US reality TV show The Real Housewives Of Beverly Hills, has not publicly addressed the incident.
Yolanda is also mother to the models Bella, 25, and Anwar, 22, who is the boyfriend of pop star Dua Lipa.
She was married to the property developer Mohamed Hadid, 72.
Gigi previously told Harper’s Bazaar that Zayn and her mother got along well.
She said, “he’s usually on my mum’s side,” adding: “So, he’s smart in that sense.”
Zayn, who previously dated Little Mix singer Perrie Edwards, launched a solo career after leaving One Direction in 2015.
His most recent album, Nobody Is Listening, peaked at 17 in the UK albums chart.
Representatives for Zayn, Yolanda and Gigi have been contacted for further comment.