Dale Williams and Larkin Cen set up their business Hokkei on Crwys Road, a year after reaching the final of the amateur cooking show in 2013.
Hokkei failed to reopen after Christmas and the company website has been taken offline.
A meeting of creditors will be held at the Hilton Hotel in Newport on 1 February.
Their venture had been covered in a four-part BBC Wales documentary called Larkin and Dale's Takeaway Revolution.
Mr Cen remained the sole director after Mr Williams resigned last summer and another director, Alan Heycock, resigned late in 2015.
CVR Global has been appointed to deal with the insolvency.
An Asian takeaway business founded by two Masterchef finalists in Cardiff has gone into administration.