Ali, 74, had been at a Phoenix hospital since Thursday with what spokesman Bob Gunnell had described as a respiratory issue.
"After a 32-year battle with Parkinson's disease, Muhammad Ali has passed away at the age of 74. The three-time World Heavyweight Champion boxer died this evening," Gunnell said in a statement. "The Ali family would like to thank everyone for their thoughts, prayers, and support and asks for privacy at this time."
Laila Ali "truly appreciates the outpouring of love for her family, as she spends quality time with her dad," a statement issued by her business manager said.
Muhammad Ali also was hospitalized in January 2015 with a urinary tract infection. He was hospitalized in December 2014 with pneumonia.
Hours before her famed father passed away, Laila Ali posted a throwback photo of Muhammad Ali with her daughter, Sydney, who was born in 2011.
"I love this photo of my father and my daughter Sydney when she was a baby! Thank for all the love and well wishes. I feel your love and appreciate it!!" Laila Ali, herself a former world champion boxer, wrote.
In recent years, Ali had largely stayed out of the public spotlight. In his last known appearance, Ali appeared at Parkinson's fundraiser April 9 in Phoenix, according to the Arizona Republic. A photo posted by the newspaper showed Ali wearing dark sunglasses.
He once was known not only for his athletic prowess as a three-time heavyweight champion but also for his social activism.
Three days with 'The Greatest'
Three days with Muhammad Ali
Ali was born in Louisville, Kentucky, as Cassius Clay in January 1942. He began boxing as an amateur when he was 12 years old and in 1964 became heavyweight champion with a knockout of Sonny Liston. That year he joined the Nation of Islam and changed his name.
Ali's sparkling career was interrupted for 3½ years in the 1960s when he refused induction into the U.S. Army during the Vietnam War and was convicted of draft evasion. The Supreme Court overturned the conviction.
He went on to win the heavyweight title twice more before retiring for good in 1981.
-CNN