Christchurch's AMI Stadium was due to host two quarter-finals plus pool matches featuring England and Scotland.
But reports have revealed there would be no guarantee that repairs to structural damage would be completed by September.
New Zealand's Rugby World Cup Minister Murray McCully revealed organisers and the government had made the decision to change venues in the face of unacceptable risks and uncertainties.
"There is also the risk of new testing exposing fresh problems and causing further delays," McCully told the BBC.
"While complete turf replacement is required, it is theoretically possible in a six month period [but] the risks are relatively high, especially if there is damage to the complex drainage of storm water systems underneath the turf."
The quarter-finals have been switched to Auckland's Eden Park while the destination of the remaining pool matches are yet to be decided.
Martin Snedden, chief executive of tournament organisers Rugby New Zealand 2011, told BBC Radio 5 Live that a decision was expected soon.
Snedden said Dunedin, Nelson and Invercargill were all potential destinations.
"A key consideration in all of this is to reschedule matches in a way that minimises the impact on other matches and therefore causes the least disruption to existing arrangements for teams and travelling," said Snedden.
Ticket-holders for the Christchurch matches will be offered a refund or tickets to the reallocated matches.
England were set to face Argentina in Christchurch in their opening Pool B match on 10 September.
The decision to move the games away from Christchurch leaves both England and the Lions' next opponents, Australia, looking for new World Cup bases.
Christchurch-born Wallabies coach Robbie Deans believes the decision is totally understandable.
"While today's news is disappointing for Christchurch, having been in the city earlier in the week and able to assess the damage for myself, the decision is understandable," said Deans
"As important as the hosting of the Rugby World Cup is to the people of New Zealand, the people of Christchurch have more important issues to deal with as they endeavour to rebuild their city and their lives after the recent tragedy."