She has also decided to appoint a number of civil servants to the board of the organisation.
In effect, the arms-length body is now under hands-on control by the Department of Culture, Arts and Leisure (DCAL) after a troubled few months.
Ms Ní Chuilín met the Sport NI board on Wednesday and said allegations about its leadership were "deeply troubling".
Nine of the organisation's 14 board members resigned on Monday, but they have yet to explain why they stood down.
Concerns have been raised about working practices within Sport NI, and at least 10 employees have made complaints.
The minister said it had been important to "act swiftly and decisively" after being made aware of the issues last week.
She added that she was introducing measures to "address the concerns raised and to reassure me" that the organisation is fit for purpose.
The chairman of Sport NI's board welcomed the minister's intervention.
Brian Henning said the board needed help, and he did not feel the appointment of senior civil servants to top positions undermined the board.
Mr Henning will remain as board chairman.
An interim executive leadership team has been appointed to take on the day-to-day running of Sport NI.
It will be headed by senior civil servant Arthur Scott, currently the director of culture at DCAL, who will act as a temporary chief executive.
An internal audit investigation shed light on issues surrounding the leadership of Sport NI.
Ms Ní Chuilín has instructed the civil servants she has sent in to implement its recommendations.
They include carrying out a confidential employee survey and a full audit of Sport NI's working culture to determine whether the allegations have a basis.
It will also begin a full review of grievances and appeals that are currently ongoing.
The minister said: "All of these actions are necessary to support Sport NI through a challenging period of change and to provide all staff with the reassurance that we have taken their views and concerns seriously."
Sports minister Carál Ní Chuilín has decided to send three civil servants to take control of Sport NI.