The 21-year-old was expected to be on the sidelines for a longer stretch after picking up the injury last week against Birmingham City, but the news comes as a boost to the Clarets as they look to secure promotion.
"It's good news so we're happy with that and Danny is as well," Burnley manager Sean Dyche told reporters. "There's nothing sinister, that's the main thing, nothing that can't be dealt with.
"There's no exact time-frame but it'll be sooner rather than later. That's what we're hoping and that's what the specialist suggested."
Ings has scored 25 times for Burnley this season.