The punishment relates to the row over whether poppies could be displayed before and during last month's match at Wembley Stadium.
Scotland themselves have been fined CHF 20,000 (£15,700), while Wales have received the same penalty and Northern Ireland must pay CHF 15,000 (£11,800) for similar offences in their matches against Serbia and Azerbaijan respectively.
"FIFA can today confirm sanctions imposed on several football associations for incidents during 2018 FIFA World Cup qualifying matches and international friendlies," read the governing body's statement on Monday.
"England has been fined CHF 45,000 for several incidents in the framework of the England v. Scotland match, including the display by the host association, the English team and spectators of a political symbol and several cases of spectator misconduct. Scotland, as the visiting association, has been fined CHF 20,000 for the display of the same political symbol and cases of misconduct committed by its own group of spectators.
"Wales has been fined CHF 20,000 and Northern Ireland CHF 15,000 in relation to several incidents, including the display of political symbols in the context of the Wales v. Serbia and Northern Ireland v. Azerbaijan matches."