England's Rugby Football Union says the Crusaders will not be able to play their Super Rugby match against the South African side the Sharks at Twickenham.
The Crusaders had contacted the England union about playing at the London venue as one of several options, with the AMI Stadium in Christchurch unavailable after being damaged in the 22 February earthquake.
The Rugby Football Union says Harlequins and Gloucester are playing nearby and they do not have the resources to run two games on the same day.
The Crusaders are playing two of their matches at Nelson's Trafalgar Park but have been looking for larger venues to draw a bigger gate.
Auckland's Eden Park has also been suggested as an option.