An X-ray has shown the full extent of the injury, which also casts doubt over Tovey's availability when the Dragons welcome Heineken Cup champions Toulouse to Rodney Parade a week later on Saturday, October 16.
"It's a real blow for us," said Dragons rugby manager Robert Beale.
"We will be treating him as often as possible to try to get him fit again as soon as we can."
Tovey was one of the region's standout performers last term, ousting New Zealander James Arlidge from the first XV as he made a hugely promising move from full back to fly-half.
His impressive form saw him touted as a potential successor to Stephen Jones at international level, with plenty of media outlets and supporters tipping him to make the summer tour to New Zealand.
Wales coach Warren Gatland decided to stick with just Jones and Dan Biggar for that two-match adventure but Tovey is expected to challenge for honours before and after next year's World Cup.
The Dragons, who begin their European campaign at Firhill on the first night of the competition, will also face former European champions London Wasps in Pool 6, meeting the English side in back-to-back fixtures in December.