Property firm Christie & Co is seeking offers in excess of £700,000 for the leasehold interest of the site, with an annual rent of £410,000.
The restaurant was first opened by Yau in 2008 but is now owned by the Kuwait-based Kout Food Group (KFG).
It is understood that KFG has decided to sell the lease to focus on other business interests.
The 165-cover noodle bar is spread across the ground and first floor of a three-storey terrace.
A second branch of Cha Cha Moon launched at the Whiteleys shopping centre in Bayswater in 2009, but closed less than a year after opening.
Simon Chaplin, head of restaurants at Christie & Co, said: “This is possibly one of the most exciting restaurant sites that has come onto the market in recent years – opportunities for operators to acquire premises in London’s West End are extremely scarce.
“We therefore expect high interest and fierce competition from both independent and corporate operators both nationally and internationally.”
Yau founded Wagamama 1992 and is also behind the Busaba Eathai chain and the Michelin-starred Hakkasan and Yauatcha restaurants.
Christie & Co is seeking the first round of offers by 25 October 2016.