Kluivert is the second son of former football player Kenneth Kluivert, who played for SV Robinhood in the SVB Hoofdklasse and for the Suriname national team.
His mother Lidwina Kluivert, was born in Willemstad, Curaçao, in the former Netherlands Antilles, to a Surinamese father and Curaçaoan mother.
His parents were married in Paramaribo, and both his elder siblings were born in Suriname, before the family emigrated to the Netherlands in 1970.

On 24 September 2007, Kluivert's wife Rossana Lima gave birth to a baby boy, named Shane Patrick.
He has three sons, Quincy, Justin and Ruben from his first marriage.
Justin Kluivert played for the Ajax Youth Academy having won the B-juniors Eredivisie, the under-17 competition in the Netherlands, and having played in the 2015 edition of the Copa Amsterdam as well.
Justin moved to Italian club A.S. Roma in 2018.
Kluivert is the second son of former football player Kenneth Kluivert, who played for SV Robinhood in the SVB Hoofdklasse and for the Suriname national team. His mother Lidwina Kluivert, was born in Willemstad, Curaçao, in the former Netherlands Antilles, to a Surinamese father and Curaçaoan mother. His parents were married in Paramaribo, and both his elder siblings were born in Suriname, before the family emigrated to the Netherlands in 1970.
On 24 September 2007, Kluivert's wife Rossana Lima gave birth to a baby boy, named Shane Patrick. He has three sons, Quincy, Justin and Ruben from his first marriage. Justin Kluivert played for the Ajax Youth Academy having won the B-juniors Eredivisie, the under-17 competition in the Netherlands, and having played in the 2015 edition of the Copa Amsterdam as well. Justin moved to Italian club A.S. Roma in 2018.
Patrick Kluivert