Burton has struggled for form since returning from a pre-season knee injury in round two.
The 32-year-old was omitted from the Crows team this week, with coach Neil Craig saying the veteran needed to regain more strength and power in his wasted leg.
A surgeon recommended Burton undergo another arthroscopy as the best course of action on Thursday.
Burton is out of contract at season’s end and this latest setback has cast more doubt over his future at AFL level.
Thompson, who has also been battling knee tendonitis, has been replaced in the side by young defender Tony Armstrong, with ruckman Jonathon Griffin and untried forward Jack Gunston the travelling emergencies.