The First Minister said “legitimate issues” had been raised by union leaders over poor pay and conditions.
And she said the festival should be in the “vanguard” of ensuring people are paid the Living Wage of £8.45 an hour.
She said: “My message to venues would be the same as it would to any employer. We live in an age where we want to see people well.”
Unite, Britain’s biggest trade union, claims many venue workers are being classed as volunteers to avoid paying them the living wage, which is said to be “almost unheard of” at the Fringe.
It is also claimed that some venue workers are being paid as little as £200 for six weeks work, with some staff having to work for 12 hours or more at a time without a break.
One SNP MP, Tommy Sheppard, has called on the Edinburgh Festival Fringe to introduce a new code of practice to try to curb “widespread” exploitation of Fringe workers, saying the issue had been “ignored for too long.”
Speaking during a visit to Castlebrae Community High, which has been turned into a venue for the Edinburgh International Festival, Ms Sturgeon said: “All of these are legitimate issues to be raising.
“I don’t speak for any of the festivals, but I know there is an appetite and a willigness to address them.
“We want the Edinburgh Festival to be not just something that people come to enjoy, but where the people providing that enjoyment are working in great conditions and getting good pay.
“I think it’s healthy, and one of the good things about the festivals, is that debates are had and these issues are brought to the fore.
“As a government, we are champions of the living wage. I think we have to work together to make sure that events like the Edinburgh Festival are in the vanguard of that kind of progress.”