It was initially unclear who long the 21-year-old would be sidelined for but the Dragons have now confirmed that Tovey will not make it back in time for their European openers.
"Jason is out for a couple of weeks", said Dragons backs coach Darren Edwards.
"The last thing we heard he was three weeks away. But we can't focus on who isn't there."
The Dragons kick-off their European campaign against Glasgow in a week's time before welcoming Toulouse to Rodney Parade on October 16.
Tovey looks certain to miss those two games but there is some good news with Ashley Smith due to return this weekend.
The 23-year-old will make the trip to Northern Italy for the Magners League encounter with Benetton Treviso with a place on the bench most likely.
"It's a big boost", added Edwards.
"He is a great communicator in attack and defence. If you are organised you defend better.
"It's great to have him back but we can't expect too much of him. And it will be the same with Jason. We can't pin everything on Jason not being there. It's a team thing that we are trying to put right."