Melanie and George were close, and she and sister Yioda were left a major part of his estate - which included a £97.6million (NZ$190m) fortune and a Grade II listed mansion in Highgate, North London - after his death.
She has spoken fondly of her brother in the past, and just days ago released a joint statement in which she told his fans that their kind messages "lift us when things are tough".
George Michael's sister Melanie Panayiotou. Photo / Supplied
In November she stood up for her brother in a magazine article, saying he was "my 'very proud to be gay' brother, contrary to what you may have read recently."
Her little brother George was found dead at his home in Goring-on-Thames, Oxfordshire, on Christmas Day 2016, aged 53. A subsequent autopsy cited an enlarged heart and fatty liver as contributory factors in his death. This can be linked to drug and alcohol abuse.
Melanie's last public words - just 48 hours before her death - were about her love for older brother George, and she and other members of her family asked that people continue to do "good deeds in his memory".
She and Yioda, his father Jack and longtime manager David Austin shared a statement on Michael's official website saying the family have "come to fully appreciate (although we already knew really), quite how much love there is out there in the world, for both Yog and his beautiful music."
They added: "We know how much his lyrics can offer support when things are tough and help celebrate when times are good and life is going well ... and that is just as powerful now as if he were still with us and as many of you say in your messages, it's a gift.
Part of the message from the official George Michael website, shared by Melanie two days before her death.
"It seems important that his generosity of spirit and natural empathy have touched you in a way that would have him embarrassed, all your kind words are really good to hear and we know you have always known his true heart."
They thanked fans for embracing the recent film Last Christmas based on Michael's music, adding that it "is going to be there to celebrate and remember Yog and his music well into the future ... and we thank everyone whose efforts brought his music to you."
His family added they "will be swerving the bad and enjoying the good as much as we can this coming year", adding that the past year has been "difficult and busy" for Michael's "hardworking team".
"We are, as usual, staying as positive as possible, which is what we and Yog would wish for you all, and we are all hoping for a peaceful 2020. (Wow 2020! - when you grew up with Yog, that used to seem so far away but, here we are folks - It's the future)!!!" they added.
Andrew Ridgeley and George Michael. Photo / Getty Images
The Metropolitan Police confirmed it had been called to a property in north-west London on Wednesday evening local time.
In a statement, the force said: "Police were called by London Ambulance Service at approximately 7.35pm on Wednesday, December 25 to reports of the sudden death of a woman, aged in her 50s, at an address in Oak Hill Park, NW3.
"The death is not being treated as suspicious by police.
"A report will be compiled for the Coroner into the circumstances."
London Ambulance Service also confirmed its attendance saying: "We sent a double crewed ambulance that arrived at the address at 7.46pm to treat one adult patient.
"Sadly, the patient had died. We then called the Metropolitan Police to request their attendance."
Lawyer John Reid said on behalf of the family: "We can confirm that very tragically Melanie has passed away suddenly.
"We would simply ask that the family' s privacy be respected at this very sad time."
George Michael performing on stage during the Japanese/Australasian leg of his Faith World Tour, 1988. Photo / Getty Images
Her cause of death is not yet known.
An auction site that has sold George Michael's outfits for charity paid tribute to Panayiotou on social media.
It said: "We are saddened to hear of the loss of Melanie Panayiotou, George's sister. Sending all our hugs and thoughts to the Panayiotou family."
Melanie had spoken proudly of her famous brother in November, telling The Big Issue about the release of the George-inspired Christmas movie Last Christmas.
She said: "My family and I hope you all enjoy the film, and Yog's music old and new, woven beautifully into this fun, easy tale of love and self-love," she wrote in the publication.
"As many of you know, Yog adored Christmas and he loved the idea of this film. I am sure he will be enjoying seeing Emilia [Clarke]'s amazing light bulb smile, something they share, across the celestial miles!
"And, most importantly, we all, together with our dear departed Yog wish a very merry, merry Christmas to Big Issue sellers and readers alike."
Melanie Panayiotou, sister of singer George Michael. Photo / Getty Images
She also dismissed Sir Elton John's claim that he was "uncomfortable" with his sexuality.
Speaking to close friend Sharon Osbourne on her American chat show, The Talk, Sir Elton claimed the late singer was "so uncomfortable in his skin about being gay even though he said he wasn't."
His sexuality had remained private until 1998, when he was arrested for performing a "lewd act" in front of an undercover police officer in a restroom at Will Rogers Memorial Park in Beverly Hills.
Singer George Michael. Photo / Getty Images
Michael and his siblings were raised in Kingsbury, London, and later Radlett, Hertfordshire, while their father Kyriacos "Jack" Panayiotou worked. His mother died in 1997, but he and his sister are survived by their father.
Michael's family called him "Yog," a nickname derived from his Greek name.
During his career, Michael enjoyed seven number ones on the UK singles charts, including Careless Whisper, A Different Corner, Jesus To A Child and Fast Love.
He had 23 top-10 hits, including Faith, Father Figure, Outside and You Have Been Loved.
Michael - whose real name was Georgios Kyriacos Panayiotou - sold more than 100 million albums throughout his career.
