The 36-year-old had already been ruled out of the Magpies' clash with the Western Bulldogs at Marvel Stadium on Friday night after pulling up sore following last week's draw against Fremantle.
But Collingwood revealed on Friday they hoped Pendlebury would be back to "full fitness" by round 15.
"Scott was cleared to train on Wednesday and while he got through most of the session, it was during the last tackling drill where he tested it and felt soreness return in that bicep," Collingwood high-performance boss Jarrod Wade said.
"It's a slight setback for Scott who will rehabilitate his bicep over the coming weeks.
"Scott is the ultimate professional and in positive news for him he will be able to keep his general fitness and remain on a running program during his recovery."
As well as the match against the Bulldogs, Pendlebury will miss the King's Birthday clash with Melbourne and a round-14 match against North Melbourne.
Collingwood have the bye in round 15 and Pendlebury will aim to return for a trip to play Gold Coast the following week.
The dual premiership player is six games away from becoming the sixth member of the VFL/AFL's 400th club.
If he returns against the Suns and plays every game from there, Pendlebury will reach the milestone against Carlton at the MCG on August 3.
This injury is another blow to the reigning premiers who are already without Jordan De Goey (abdominal), Tom Mitchell (foot), Brody Mihocek (hamstring), Jamie Elliott (vascular), Will Hoskin-Elliott (hamstring) and Mason Cox (knee).
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