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."

Under the proposed legislation, first-time offenders who do not cause serious injury will face a maximum of 15 days police custody instead of up to two years in jail.
It now needs the approval of the upper house and President Vladimir Putin.
Campaigners say the bill - dubbed the "slapping law" - would mean the "exoneration of tyrants in the home".
The State Duma voted 380-3 for the bill, two days after it passed its second reading.
The bill, drafted by MP Olga Batalina, concerns assaults that inflict physical pain but do not cause bodily injury that threatens the victim's health.
It followed a change in the criminal code in July which decriminalised battery against strangers, but made battery within the family a criminal offence.
Conservatives argued that it was unacceptable that parents could therefore face harsher penalties for smacking their children than a neighbour would.
Under the bill, the first offence would be considered administrative rather than criminal and punished with a fine of up to 30,000 rubles (£400; €470), detention of up to 15 days or compulsory community service up to 120 hours.
Assaults causing serious injury or repeat offences within a year would still be criminal offences and carry potential jail terms.
"We want to show that Russian deputies will not allow the same excesses present in Western Europe," said ruling party lawmaker Andrei Isayev, claiming that European children "inform on their parents" in order to get their way, which leads to the parents losing custody.
But MPs from the Communist Party opposed the bill.
"Women don't often go to the police or the courts regarding their abusive husbands, now there will be even fewer such cases, and the number of murders will increase," said lawmaker Yury Sinelshchikov.
On Wednesday, Maria Mokhova, the executive director of the Sisters crisis centre for abuse victims, told Reuters: "This law calls for the exoneration of tyrants in the home.
"The message is: 'Let's not punish a person who at home beat up his family, just because he has the right to do that.'"
Russian interior ministry statistics show that 9,800 women died as a result of a serious assault in 2015, and that a quarter of murders and serious assaults take place in the home.
A petition launched by women's rights activist Alena Popova calling for comprehensive legislation against domestic violence has reached nearly 239,000 signatures.
Sports minister Carál Ní Chuilín has decided to send three civil servants to take control of Sport NI.
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Russia's lower house of parliament has passed a bill to decriminalise some forms of domestic violence.