The defender wore the skipper's armband in the 4-1 friendly victory over Altrincham on Saturday.
Shackell, 28, joined from Derby on a four-year contract earlier this month and counts Norwich, Wolves and Barnsley among his former clubs.
"It's Jason's natural role and I think he has settled into it really well," said boss Eddie Howe on Burnley's official website. "He has everyone's respect here and I think we saw immediately what a good player he is."
There was bad news for the Clarets at Moss Lane as Marvin Bartley suffered a recurrence of an ankle injury, meaning he is likely to miss all of their pre-season games.
Howe explained: "Marvin has had this nagging problem for a while now, going back to the back end of last season. He felt an ache in his ankle and went for a scan and then rested it through the summer, with a little bit of rehab, but it has come back."