Flack was found dead at the age of 40 at her home in east London on Saturday, after taking her own life.
Saturday night's highlights edition of the ITV2 dating show was pulled, and there has been speculation about whether the rest of the series would air.
It has now been confirmed that although it will not be on tonight, Love Island will be back on Monday, with a tribute to Flack.
"All of us are absolutely devastated at this tragic news.
"After careful consultation between Caroline's representatives and the Love Island production team and given how close we still are to the news of Caroline's tragic death we have decided not to broadcast tonight's Love Island out of respect for Caroline's family.
Flack's family confirmed that she died on Saturday, adding in a statement: "We would ask that the press respect the privacy of the family at this difficult time and we would ask they make no attempt to contact us and/or photograph us."
Ambulance crews were called on Friday night to a property in the street in Clapton, north east London, where Flack was thought to have recently moved but a London Ambulance Service spokesman refused to confirm or deny reports the paramedics attended her flat.
An LAS statement said: "We were called shortly after 10.30pm on 14 February to a residential property on Northwold Road, N16.
"Crews attended and, following a clinical assessment, the person was not taken to hospital. Due to patient confidentiality we cannot comment further."
The LAS also said crews were called to Northwold Road at 2.30pm on Saturday, adding that "a person was pronounced dead at the scene", but would not comment on whether the two incidents were linked.
The shock news prompted a flood of tributes from celebrities but also questions about the decision to press ahead with prosecuting Flack for her alleged assault on boyfriend Lewis Burton, as well as the pressures faced by TV celebrities from the press and social media.
Flack, who was described as "vulnerable" by her management, stepped down from presenting the current winter series of Love Island after she was alleged to have assaulted Burton at her then-flat in Islington, north London, in December.
She entered a not guilty plea to the assault charge at Highbury Corner Magistrates' Court and was released on bail, with conditions that stopped her having contact with her boyfriend ahead of a trial in March.
Her management company criticised the Crown Prosecution Service (CPS) for pressing ahead with what it called her "show trial" even after her boyfriend said he did not support it.
By Sunday evening, an online petition calling for a Government inquiry into "the practices and policies of mainstream media organisations and social media platforms in their efforts to protect members of the public from harm" had more than 200,000 signatures.
The tragedy has put the spotlight back on the pressures which come with TV celebrity.
Flack is the fourth person linked to the ITV2 dating programme to have killed themselves.
Sophie Gradon, who was a contestant in 2016, was found dead at her home in 2018 at the age of 32.
Her boyfriend Aaron Armstrong, who had found her body, killed himself three weeks later. He was 25.
Mike Thalassitis, who appeared in the 2017 series, was 26 when he was found dead in a park in March last year.
Tributes to Flack poured in after her death, with Burton saying that his "heart is broken".
He said in an emotional message on Instagram that he would now be Flack's "voice" and would "get all the answers".
Beside a picture of them together, he wrote: "My heart is broken we had something so special.
"I am so lost for words I am in so much pain I miss you so much I know you felt safe with me you always said I don't think about anything else when I am with you and I was not allowed to be there this time I kept asking and asking."
Burton, 27, added: "I will be your voice baby I promise I will ask all the questions you wanted and I will get all the answers nothing will bring you back but I will try make you proud everyday.
"I love you with all my heart."
Flack's former X Factor colleague Dermot O'Leary said he had "candles lit" in her memory, and her Love Island colleague Iain Stirling, the programme's narrator, shared a video of Flack from a performance on Strictly Come Dancing in 2014 and wrote: "Today my friend slow motion walked into heaven. I will miss her always. Thank you for everything x."
Laura Whitmore, who replaced Flack as Love Island host for the latest series, tweeted "I'm trying to find the words but I can't", followed by a broken heart emoji.