The Icelandic international was subbed in the first half of City's win over Bristol City on Sunday. He was replaced by Joe Mason who could look to start against Brighton tomorrow.
"He (Gunnarsson) Should be about a week or so," confirmed Mackay. "It's not as bad as we thought it would be considering the way he limped off."
Cardiff face Brighton (Aug 17th), Burnley (Aug 20th), Huddersfield (Aug 23rd) and Portsmouth (Aug 27th).
With Portsmouth the most likely target for Gunnarsson's return.