Police say they were called to an address near Wrotham, Kent following a report of concern for the welfare of a woman on Monday afternoon.
The woman, aged 25, was later pronounced dead by South East Coast Ambulance Service.
"At this stage, the death is being treated as unexplained and sudden," said a statement from Kent Police.
Geldof was pictured at a fashion show in London last week
Born in 1989, Peaches Honeyblossom Geldof embarked on a media career at the age of 15, when she began writing a column for Elle magazine.
She left home at sixteen and went on to contribute to the Telegraph and the Guardian, and presented TV shows including ITV2's OMG! with Peaches Geldof.
She also worked as a model and, just last week, attended a launch for Tesco's F&F clothing range in London.
She was married to musician Thomas Cohen, with whom she had two sons, Astala, one, and Phaedra, who will turn one on 24 April.
Geldof lost her own mother when she was just 11 years old. Paula Yates died of a drug overdose in September 2000.
Speaking to Elle Magazine in 2012, Peaches said she had not come to terms with Yates's death for several years.
"I remember the day my mother died, and it's still hard to talk about it. I just blocked it out. I went to school the next day because my father's mentality was 'keep calm and carry on'," she said.
"So we all went to school and tried to act as if nothing had happened. But it had happened. I didn't grieve. I didn't cry at her funeral. I couldn't express anything because I was just numb to it all. I didn't start grieving for my mother properly until I was maybe 16."
Geldof said she had experimented with drugs as a teenager, but was "never that wild".
She was previously married to rock musician Max Drummey but the pair separated in 2009 after a six-month marriage.
Her last tweet, posted on Sunday was a picture of her as a Baby
in her mother's arms.
She leaves her husband and sons; father Bob Geldof; sisters Fifi Trixibelle and Pixie; and younger half-sister, Tiger Lily Hutchence Geldof.http://www.bbc.co.uk/news/uk-26931337