The 31-year-old plunged from the third floor of the Casa Sur Hotel in the trendy Palermo neighbourhood resulting in "extremely serious injuries", according to authorities in the South American country's capital. He was pronounced dead at the scene.
The circumstances around his death are still being investigated.
Alberto Crescenti, head of the state emergency medical system, said on Argentina's Todo Noticias TV channel Payne fell into a courtyard of the hotel.
The singer was in the city to support his former bandmate Niall Horan whose world tour included dates in Argentina, having been seen dancing at his show two weeks ago at the Movistar Arena alongside his girlfriend Kate Cassidy.
US outlet TMZ reported Payne had been acting erratically in the hotel lobby and smashed a laptop before going back to his third floor room.
Citing officials, leading local newspapers La Nacion and Clarin reported police were called to the hotel responding to an emergency call that cited "an aggressive man who could be under the effects of drugs and alcohol."
Ambulance workers later confirmed the death of the singer, who was found in an interior hotel patio, according to the news reports.
One Direction became one of the biggest pop groups in the world with five albums and four world tours after being put together by Simon Cowell on the X-Factor in 2010.
Payne was one of the founding members alongside Harry Styles, Zayn Malik, Niall Horan and Louis Tomlinson.
The band went on indefinite hiatus after Malik announced his departure in 2015.
Payne released his debut solo album LP1 in December 2019 which included the singles Polaroid and Familiar.
The Wolverhampton-born singer dated former Girls Aloud star Cheryl Cole after the band broke up and they had a son, Bear, born in 2017, but he had been in a relationship with Cassidy since 2022. He is also survived by his parents, Geoff and Karen Payne, and his two older sisters, Ruth and Nicola.