Asked about the proposal for such an organisation to be created by SNP MSP James Dornan, in response to the Orange Order marches in Glasgow last weekend, Ms Sturgeon said she would ask the justice secretary to “consider the possible creation of a Parades Commission”.
In Northern Ireland, the Parades Commission is a quasi-judicial decision-making body that determines whether restrictions should be placed on contentious marches.
It is made up by independent members and considers submissions from both sides.
Ms Sturgeon told MSPs: “In regard to the specific proposal of a Parades Commission, yes, I am happy that the government gives that further consideration.
"I have already asked the justice secretary to consider what further action could be taken to maintain the important balance of rights between peaceful procession, freedom of speech, but also the ability of people to go about their daily lives without feeling unsafe and being free from harassment.
"I’ll ask the justice secretary to consider the possible creation of a Parades Commission as part of that."
It comes less than a week after thousands of people took part in processions on Saturday which shut down city centre roads and prompted counter-protests, with the marches also passing by Catholic churches on their routes.
Police arrested 14 people during the Orange Order marches, including for “sectarian-related breach of the peace”, as well as anti-social behaviour and public disorder.
The marches led to a condemnation by Police Scotland of “outbreaks of racist and sectarian singing” by some supporting the processions.
Police said they were investigating a number of “hateful” videos showing this.
During First Minister’s Questions on Thursday, Ms Sturgeon said Scotland should show “zero tolerance” towards sectarian abuse and “anti-Catholic bigotry”.
The SNP leader said: “I think it is important to stress that peaceful public assembly and freedom of expression are fundamentally important rights and I know we are all committed to upholding these.
"But it is also a fundamental right of any person and any community to go about their daily business without fears for their safety.
"I know that members will join me in unequivocally condemning of anti-Catholic bigotry, which we have seen on our streets in recent times.
"There is no place for it in a modern Scotland and we must all show zero tolerance towards it.
"In terms of the specific proposal, I can confirm that we will give that consideration and we will report back to Parliament further in due course.”
Following the marches last weekend, chief superintendent Mark Sutherland, divisional commander for Greater Glasgow, said: “Once again, we see a number of people intent in causing offence and stirring up hatred by singing unacceptable sectarian and racist songs. I want to again condemn this behaviour in the strongest possible terms.
“It is clear that sectarianism remains a serious, ongoing problem in Scotland and whilst policing has an important role in tackling this type of behaviour, this is a collective problem and needs to be addressed in a collective, collaborative manner.”