The administrators at Deloitte have said the 16 Gaucho sites will remain open while a buyer is sought for that part of the business.
Cau has experienced falling sales for three years, and is now making significant losses, but the Gaucho business is still profitable.
Gaucho at St Andrew Square remains at risk with Cau on Castle Street set to close.
Matt Smith, joint administrator at Deloitte, said: “Unfortunately the Cau brand has struggled in the oversupplied casual dining sector, with rapid over-expansion, poor site selection, onerous lease arrangements and a fundamentally poor guest proposition all being factors in its under-performance.
“As such, the decision has been made to close this loss-making part of the group with immediate effect, unfortunately resulting in today’s redundancies.”
Mr Smith said Gaucho was still trading well and had strong customer loyalty.
The restaurant group has 1,305 employees in total, with 540 at Cau, 714 at Gaucho and 51 at the company’s head office.
Gaucho is the latest in a string of consumer-facing business to face strain on the high street, with the likes of Prezzo, Byron and Jamie’s Italian all shutting restaurants and axing hundreds of jobs.
Hummus Bros, a London food chain, also went into administration this summer.
Robert Hayton, dead of UK business rates at real estate adviser Altus Group, said: “There has been huge growth in the casual dining market with restaurant numbers up 16% overall since 2010. The race for space has pushed up rents impacting on rateable values.
“Extra tax for business rates coupled with rising food prices and staff costs through increases in both the national and minimum wages are creating a potentially lethal cocktail as margins are squeezed.”