The Uruguay midfielder was given the suspension, which relates to domestic games, by an independent commission on November 18 and Spurs indicated they would appeal.
The FA has now confirmed an appeal board has dismissed Tottenham's challenge and Bentancur will serve the remainder of his ban, missing matches against Manchester United in the League Cup and Liverpool in the Premier League.
"This appeal was dismissed following a hearing, and the seven-match suspension remains as ordered by the regulatory commission," the governing body said in a statement.
Bentancur was charged with misconduct in September over a television interview he gave in his home country in June, with the reference to South Korea star Son's race making it an aggravated breach.
The midfielder was asked during the interview to show the shirt of a Spurs player, and replied: "Sonny's? It could be Sonny's cousin too as they all look the same."
The standard minimum ban where such a breach is established is six matches, but Spurs said they felt the sanction was "severe" when confirming their intention to appeal.
Bentancur apologised on Instagram to Son for his remarks and Son accepted that apology in a statement on the same platform.
Bentancur was also fined £100,000 ($127,000).
