The Belgian playmaker has missed Spurs' last eight matches with a niggling hip injury but had hoped to be fit in time for the Emirates Stadium clash.
Villas-Boas said he hoped the 25-year-old would not need surgery to rectify the problem but may still not be ready in time for next week's Europa League trip to Lazio.
Villas-Boas said: "Dembele does not have a chance, not for this game. There is a 50% chance he will be back for the Lazio game.
"I think surgery at the moment is out of the question, hopefully."
Villas-Boas also gave updates on Jermain Defoe, Kyle Walker and Aaron Lennon, who all suffered hamstring injuries in last week's 2-1 defeat to Manchester City, with the latter most likely to be ready to face the Gunners.
"They haven't trained with the team yet. They have had lighter sessions on their own," Villas-Boas said of the trio.
"We will have to see today how they return to see if there's any disturbance. Lennon had a scan yesterday, and it's fine on his hamstring."