In a short clip posted on social media this week from Uruguayan Television programme Por La Camiseta, host Rafa Cotelo asks the Uruguay international for a Spurs player's shirt, to which Bentancur replies, "Sonny's?", adding: "It could be Sonny's cousin too as they all look the same."
Bentancur apologised after his comments were met with disapproval.
"Sonny brother! I apologise to you for what happened, it was just a very bad joke," the 26-year-old wrote on his Instagram stories on Friday.
"You know I love you and I would never disrespect you or hurt you or anyone else! I love you, brother!"
Uruguay are in Group C with the United States, Panama and Bolivia in the Copa America, which will run from Thursday to July 14 in the US.
South Korea have advanced to the third round of Asia's 2026 World Cup qualifiers starting on June 27.