"She passed peacefully at 1:17 p.m. surrounded by family and close friends," Melissa Rivers said in a written statement.
The funeral for Rivers will be at Temple Emanu-El in Manhattan on Sunday, according to temple spokeswoman Elizabeth Fezrine. Details, including the time and if the public will be allowed to attend, are not yet known, she said.
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Rivers, 81, had been on life support at Manhattan's Mount Sinai hospital, where she was taken after she stopped breathing at the Yorkville Endoscopy clinic last Thursday.
Rivers was undergoing an apparently minor elective procedure at the clinic when she suffered cardiac and respiratory arrest, according to the New York Fire Department.
Paramedics took her by ambulance to Mount Sinai Hospital, about a mile from the clinic, where she was initially listed in critical condition.
The outpatient clinic is now being investigated by the New York State Department of Health, spokesman James O'Hara said.
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Her death also has triggered an investigation by the New York medical examiner's office, its spokeswoman, Julie Bolcer, told CNN. "The cause and manner of death will be announced at some point," she said.
The Rivers family made very little information about her medical condition public, finally confirming Tuesday that she was on life support.
"My son and I would like to thank the doctors, nurses, and staff of Mount Sinai Hospital for the amazing care they provided for my mother," her daughter said. "Cooper and I have found ourselves humbled by the outpouring of love, support, and prayers we have received from around the world. They have been heard and appreciated.'
Melissa Rivers and her son Cooper have spent the past week by Rivers' hospital bedside, rushing there last Thursday when they learned of her illness.
'My mother's greatest joy in life was to make people laugh," Melissa Rivers said. "Although that is difficult to do right now, I know her final wish would be that we return to laughing soon."
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The clinic has not responded to repeated calls from CNN about the state's investigation.
Yorkville Endoscopy's website says it is an "ambulatory surgical center" that has been "approved by the Department of Health." The description of its accreditations is blank.
"Yorkville Endoscopy is a state of the art facility, staffed by highly experienced endoscopists whose mission is to provide safe and compassionate care to patients and their families," the website says.