Stannard fracture a bone in his back during the Ghent-Wevelgem race on Sunday and is out of the Spring Classics.
Andre Greipel also saw his Classics season ended in the same race, although in a different incident to Stannard's.
"You can't rush an injury like this. I've got to rest," Britain's Stannard told the Team Sky website.
"Once I've spoken to the specialist, I'll have a better idea of what I can and can't do. Then I'll be able to focus on my recovery.
"It's going to be really hard to watch them (Paris-Roubaix and the Tour of Flanders) on TV," he said.
"To be honest, I haven't had time to really think about it yet because it's been pretty painful 24 hours. They are only bike races at the end of the day and there'll be plenty more chances to ride them in the future."
- Sports & Recreation