Ballard had a scan on the injury earlier today, with assistant head coach Luciano Vulcano hoping the defender will "only be out for a short time".
Ballard was forced off inside 10 minutes at Burnley on Saturday after suffering the injury in an innocuous incident when he went up to head the ball.
Sunderland and Ballard are now hoping for good news, with the defender having endured his fair share of injury frustration during his time on Wearside. Ballard missed 24 Championship games last season, but is a hugely important figure in Regis Le Bris' side.
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"Ballard is having a scan today," said Vulcano, who spoke to the media on Monday afternoon.
"We will know more information about it in the next few hours.
"Hopefully, we all hope that he will be out for a short time, because we need him and all the players with us."
Sunderland kick-off their Carabao Cup campaign at home to Huddersfield Town on Tuesday night, and while changes to the starting XI are inevitable, Vulcano says boss Regis Le Bris will name a strong side.
"We respect every match we will face, so, for sure, tomorrow will be a good starting XI," he said.
"Regis is thinking about these things.
"In the next few hours, he will decide for sure. But we will respect the cup, because it's really important.
"Maybe some players will have some chances. We will see which one will be his decision in the next hours."
Premier League survival is the priority for Sunderland this season, but the [Black Cats](http://www.thenorthernecho.co.uk/sport/football/sunderland) will still take the Carabao Cup seriously.
Vulcano said: "I think every match is an opportunity for us to show our style of play, our commitment to the badge for our fans.
"We want to go to the next chapter every time and try to improve our results and our football.
"Yes, for sure, we want to go to the next chapter, also in the cup. We will try our best, obviously. We can win, we can lose, but we will try for sure."