Cast and crew are currently self-isolating for 14 days in line with Government guidance.
A spokesperson for Sky said: “Throughout this time, the safety of our colleagues and customers remains our number one priority.
“Brassic production has paused with cast and crew now self-isolating. We will return to production as soon as it is safe to do so.”
Sky did not confirm the identity of the person who tested positive.
Created by This Is England actor Joe Gilgun and Shameless writer Danny Brocklehurst, Brassic follows a group of cash-strapped working class friends living in the fictional village of Hawley.
Michelle Keegan plays Erin, a young woman whose troubled childhood leads to a wild teenage phase and an unplanned pregnancy.
The first series, which aired in 2019, received generally positive reviews, with the second series airing in May.
Last week, filming for Coronation Street was temporarily disrupted after a member of the cast tested positive for coronavirus.
Earlier this month, filming on The Batman, starring Robert Pattinson, was temporarily halted after a member of the production team tested positive.
US outlets Variety and Vanity Fair previously reported it was Pattinson, but a Warner Bros spokeswoman refused to confirm their identity.
