The Football Association had hoped to face the South American side at the Parken Stadium on Wednesday February 9.
Despite booking the stadium the FA had not cleared the game with their Danish counterparts, who would not sanction an international friendly in their country at the same time their national team were playing.
They said the game could only go ahead if played 24 hours earlier, but Argentina do not think their players could all get to the Scandinavian country in time to recover from jetlag and play. The FA are believed to be searching for new opponents.