Mears was forced off the field during his side's Heineken Cup defeat to Ulster at Ravenhill, with tests since confirming that he suffered medial ligament damage to his left knee.
The 30-year-old, who started the first Test for the Lions against the Springboks this summer, is expected to be out of action for between six and eight weeks.
A likely return date of early-mid December could see Mears feature in Bath's European double header with Edinburgh.
With 34 England caps to his name and the experience of a Lions tour behind him, Mears had been expected to be a key part of Martin Johnson's plans ahead of their clash with the Wallabies at Twiockenham on November 7.
His withdrawal means he becomes the latest in a long line of English absentees after the likes of fellow Lions Riki Flutey, Andrew Sheridan, full back Delon Armitage fly-half Danny Cipriani, flanker Tom Rees and centre Jordan Turner-Hall were all forced out of contention.