Eric Dier was one of three England players to wear the socks, which have white dots around the ankles
The FA has been fined 70,000 Swiss francs (£50,000) after Dele Alli, Eric Dier and Raheem Sterling wore "unauthorised" socks at the World Cup.
The players wore branded ankle support socks over official Nike socks, ignoring a Fifa warning to stop.
Fifa said the FA's fine was for "breaching media and marketing regulations and the Fifa equipment regulations".
The fine followed England's quarter-final win over Sweden.
Fifa said several England players "continued to display unauthorised commercial branding on playing equipment items before and during the quarter-final match between Sweden and England".
The Swedish FA has also been punished with the same fine for a similar sock offence earlier in the tournament.
That makes it the joint second highest fine at the World Cup behind Argentina's 105,000 Swiss franc (£80,000) punishment after their fans threw objects and chanted homophobic abuse.
-- Courtesy of BBC Sport