Engineers were working to solve the problem, but it is understood it could take two days to restore supplies.
Scotia Gas Networks said it was a "major incident" and warned people not to try to use gas appliances until the situation was resolved. An emergency centre was being set up to give people up-to-date information and hand out electric heaters to customers, particularly elderly people, who have lost their central heating.
Householders noticed problems with their gas yesterday evening. At first, around 300 homes in North Gyle and West Craigs were affected, but by this morning the problem had spread to 700 homes in a wider area.
SGN issued an emergency number - 0845 0701432.