The former Arsenal man signed for the Swans for a fee in the region of £1 million and made his debut in the League Cup tie against Barnsley on August 28. However, just a couple of days later he picked up the injury and could now be out until December.
Speaking to the club’s official website, Bartley said: "It's a strange one because I picked it up in training but I don't know how I did it. I didn't feel any pain at the time.
"I've reached the five-week stage today, I've been for a scan recently and I was told it was coming along well.
"I've got another eight weeks of recovery ahead of me, so I am getting there. It wasn't too bad in the first couple of weeks, but then you're out of the group and in the gym on your own a lot.
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"But I'll continue working away in the gym, along with receiving massages and physio work to help my recovery. I'll have another scan in a couple of weeks and hopefully that will be another good round of news."