The US part of Malik’s tour was due to also visit Las Vegas, Los Angeles, and Washington DC, ending in New York on 3 November.
He has told fans on X the dates would be rescheduled for January and the tickets will remain valid for the new dates.
“Love you all and thank you for your understanding,” he added.
On Thursday, Malik paid tribute to Payne, saying he would “cherish all the memories I have with you in my heart forever”.
“I lost a brother when you left us and can’t explain to you what I’d give to just give you a hug one last time and say goodbye to you properly and tell you that I loved and respected you dearly,” he said.
Payne and Malik rose to global fame as part of the boyband One Direction – created on the X Factor TV show in 2010 – and sang together with bandmates Harry Styles, Louis Tomlinson, and Niall Horan.
The cancellation of Malik’s US shows comes as Payne’s father, Geoff Payne, viewed tributes for his son outside the Casa Sur hotel in Buenos Aires.
He was followed by a scrum of photographers as he visited the hotel, prompting fans to shout at the press and attempt to block the building’s entrance to stop them entering.
