The chain has announced the closures this morning as part of a rescue deal.
If the plan is approved, 2,000 House of Fraser jobs will go, along with 4,000 brand and concession roles.
All the stores scheduled for closure - including the Doncaster branch in Baxtergate - will stay open until early 2019, the company has said.
The retailer needs the approval of 75% of its creditors to go ahead and they will vote on the insolvency plan, which involves company voluntary arrangements (CVAs), on 22 June.
House of Fraser chairman Frank Slevin said: "The retail industry is undergoing fundamental change and House of Fraser urgently needs to adapt to this fast-changing landscape in order to give it a future and allow it to thrive.
"Our legacy store estate has created an unsustainable cost base which, without restructuring, presents an existential threat to the business."
Closing stores was "a very difficult decision", he said, but "there should be no doubt that it is absolutely necessary if we are to continue to trade and be competitive".
Accountancy firm KPMG, which is overseeing the insolvency process, said the firm had been hit by "mounting pressures facing the UK High Street".
The Doncaster branch became a House of Fraser discount outlet store in 2008 after trading as department store Binns for several decades.
The retail giant started life back in 1849 as a small drapery shop in Glasgow and during the 1970s rapidly expanded, buying drapers across Scotland, Ireland and England as well as other department stores and Army and Navy stores as well as iconic luxury store Harrods in 1959.
The Doncaster branch opened in the mid-70s on the site of the former Owen and Owen store.