The announcement by the British Olympic Association (BOA) was made with the knowledge of the English Football Association, but came as a shock to the Scottish, Welsh and Northern Irish FAs.
SFA chief executive Stewart Regan said: "We are very surprised and disappointed."
The SFA believes that fielding a British football team will damage their standing in the eyes of the governing body for international football, FIFA.
Traditionally Scotland, Northern Ireland and Wales have all competed individually in the European Championships and in the World Cup.
The fear is that if they are seen to be joining forces with England to create a Team GB for the Olympics, FIFA may be tempted to force the nations together for other international championships in the future.
The BOA has said that any player can turn down an invitation to play.
It is unlikely that a player from Scotland would be prepared to go against the wishes of their home nation and accept the invitation - although turning down an opportunity to appear on the world stage would be hard for some.
Scots such as Julie Fleeting and Kim Little in the women's game would be certainties to play for a British women's team. For them, the Olympics could be the most high-profile tournament they ever compete in.
Some believe the hurried announcement has been made in order to generate interest in Olympic football ticket sales. A total of 1.7million 2012 football tickets go on sale this Friday. Matches will take place all around the UK including eight at Hampden Park in Glasgow.