His death was confirmed by Gayton McKenzie, South Africa's minister of sport, arts and culture, in a statement on Saturday.
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"It is with profound shock and a heavy heart that I have learnt of the passing of Jayden Adams, midfielder for Mamelodi Sundowns and Bafana Bafana, at the age of 25," McKenzie posted on X.
"South African football has lost one of its brightest young talents, and our nation mourns alongside his family, his team-mates and the millions of supporters."
Adams helped South Africa reach the World Cup knockout stage for the first time.
Further details of his death were not given.
"The cause of Jayden's passing has not yet been confirmed," McKenzie said. "I wish to appeal to members of the media and the public to exercise restraint and compassion, and to refrain from speculation."
Adams started South Africa's first Group A game against the Czech Republic and was substituted at halftime. McKenzie said he played that game only hours after learning that his grandmother had died.
Adams played several seasons for Stellenbosch before joining Mamelodi Sundowns last year. He helped the club win the CAF (African) Champions League this year.
"Death has cruelly stolen one of our own. It has robbed our nation of a remarkable footballer," the South African Football Players Union posted on X. "We will forever remember his humility, his extraordinary talent and the pride with which he represented South Africa. Rest in eternal peace, Jayden. You will never be forgotten."
South Africa's President Cyril Ramaphosa and the South African Federation of Trade Unions also expressed their condolences.