Creative Scotland chief executive Janet Archer said allowing the arts world to express opinions on the subject of the future of Scotland was 'hugely important'.
The body has an annual budget of almost £100m.
Her pledge came 24 hours after Sir Jonathan Mills, the director of the Edinburgh International Festival, said shows about Scotland's referendum would not be included in next year's festival.
He said he wanted the festival to continue to be "a politically neutral space for artists".
However, Ms Archer said: "Artists are their own artists, and we fund artists to have voice and opinion and to generate ideas and imagine the world in any way they choose to.
"I think in a context like this, where there is a heightened political environment, debate is really vital."
Ms Archer said the extension of the vote to 16-year-olds made debate and discussion through the arts particularly important.
She added: "In Scotland for the first time, younger people are going to get the vote, which is momentous.
"It's critical we engage in discussion and thinking, and if art and artists can help offer a sense of engagement with that discussion, then that is a brilliant thing.
"Creative Scotland does not have a position on the referendum, but also we do not have an opinion on what artists should do - artists should be free to realise their own imaginations.
Ms Archer also said the body would be looking more at investigating how companies and artists at the Fringe can be more "resilient" in the festival economy.
"It's a competitive environment, but that may not be a bad thing because the world is a competitive environment," she said.
"When I was at the Arts Council in England, we used to say if you can survive at the Fringe, you can survive anywhere. It is a very good place to cut your teeth and figure out how you want to do things."
Ms Archer also announced that Iain Munro, a director of creative development, would become the new deputy chief executive of the cultural funding body.
She also said the Creative Scotland files on the credit card fraud that led to more than £104,000 being fraudulently spent on a company credit card two years ago are now in the hands of the police.
She confirmed £30,000 of the defrauded sum, stolen in 2011, will not be re-imbursed by JP Morgan, the credit card supplier, and is now lost.
"I made the decision to share the audit reports with the police, and they are reviewing the files," she said.
"Whether or not it is viable to catch someone, two years on, is a question, but the right thing to do is to be open and share everything with the police.
"We won't get the rest of the money back, that is lost and we have to accept that is the case and make sure it never happens again."
She said Mr Munro, who was interim chief executive following the resignation of Andrew Dixon last year before Ms Archer's appointment, is to have a chief operating officer role.
Ms Archer added: "It is about looking at finance, operations, systems and processes, and it is about drawing together all the intelligence in the organisation.
"He did a tremendous job as acting chief executive, he was very well received in the role and he and I learned very quickly we could work together."
Ms Archer said internal organisation needed to be addressed, with five of the nine senior staff in temporary positions, which "was not an ideal position for us to be in".
A new grant management and information system will be put in place later this year.