The deal marks the latest incursion by a Chinese group into a fashion world long dominated by European players like conglomerate LVMH, owner of Louis Vuitton.
Chinese consumers are the biggest buyers of luxury goods worldwide and so far the trade war with the United States has not dented that demand.
Carven's buyout follows a series of recent attempts by retailers to restore once-prestigious labels to their former glory, banking on the resonance of their brand names.
The label was founded in 1945 by Carmen de Tommaso, alias Marie-Louise Carven, who died in 2015 at the age of 105.
Its pink chequer dresses were a hit in the 1950s and it designed uniforms for Air France flight attendants in the 1970s, before it fell on hard times in the following decade.
Carven made a comeback in 2010 under designer Guillaume Henry, dressing the likes of Alexa Chung, but the label struggled to recover from his departure in 2014, and annual sales halved to around 20 million euros ($23 million) in 2017, according to a person familiar with the business.
The company, then controlled by its Asian distributor Bluebell, filed for bankruptcy protection in May.
It had attracted bids from other French groups, but Icicle was prepared to put more money into refloating the business, a judicial source said.
Icicle has its own brand in China, and the group said its retail turnover in 2017 - which includes sales through third parties like department stores - was 204 million euros.
China's Fosun also muscled into the industry this year, acquiring high-end French label Lanvin, and peer Shandong Ruyi bought Swiss shoemaker Bally, at a time when U.S. groups like Michael Kors, which swooped on Italy's Versace, are also trying to gain a foothold in luxury.
Resurrecting brands has not always proved easy. But LVMH is putting its might behind the relaunch of 1912 label Jean Patou, hiring Carven's former star designer Henry for the job in September.
France's Poiret, a label founded at the turn of the 20th century by Paul Poiret, turned out its first catwalk collection in 90 years in February, backed by South Korean fashion group Shinsegae International.
(Reporting by Pascale Denis and Emmanuel Jarry, Writing by Sarah White; Editing by Elaine Hardcastle)