England take on world champions Spain at Wembley, while Wales play Norway in Cardiff, on Saturday. Scotland are playing a friendly in Cyprus on Friday.
The British Government, backed by the English FA, asked FIFA for permission to wear the poppies, which are the British symbol for remembering members of the armed forces who died in the line of duty.
Remembrance Day falls on November 11, the anniversary of the day the Armistice was signed marking the end of the First World War in 1918.
However, FIFA rejected the appeal in a letter to the FA.
"We regret to inform you that accepting such initiatives would open the door to similar initiatives from all over the world, jeopardising the neutrality of football," FIFA wrote.
"Therefore, we confirm herewith that the suggested embroidery on the match shirt cannot be authorised.
"There are a variety of options where the FA can continue supporting the cause of Remembrance. One of them already was approved by FIFA, the Period of Silence."
World football's governing body have allowed a minute's silence to be held before the games and for the teams to wear poppies on their training kits.
FIFA's rules prevent items of a political nature being worn on shirts and although it does not regard poppies as political, FIFA are concerned it would open the door to countries wanting to wear various different emblems on their shirts.
British sports minister Hugh Robertson wrote to FIFA urging them to re-think their decision, stating that while they understood FIFA's rules, wearing the poppy did not contravene them.
"We fully understand, and respect, FIFA's rules on its member nations not adorning their shirts with 'commercial', 'political', or 'religious' symbols or messages.
"However, the British public feel very strongly about this issue which is seen as an act of national remembrance to commemorate those who gave their lives in the service of their country. It is not religious or political in any way."
Scotland players will also wear a poppy on their training kit ahead of their friendly against Cyprus in Larnaca on Friday.
