Roberts, who played a starring role in Wales' march to the World Cup semi-finals, was forced to limp off in the early stages of the Blues' impressive 26-20 victory over Racing Metro in Paris last Friday.
The 2009 Lions tourist has undergone a scan on the problem, and while the Blues are still awaiting the results, Burnell says Roberts will not be available against the Exiles at Cardiff City Stadium.
But the giant three-quarter will be fit in time for Wales' Millennium Stadium clash with Australia on December 3.
Burnell said: "Jamie twisted his knee in a tackle in Paris. He went for a scan yesterday and we are still waiting for the results but our physios are confident that there is nothing serious there, and he is running on it already.
"He will not be fit for this week but he will be fit if he needs a game against Aironi next week and he is going to be fit for Wales."
Burnell also confirmed that lock James Down will be out for six months after he suffered a fracture and dislocation of his ankle against Racing Metro.