Deloitte said the shops would continue to trade but the closures were expected over the next one to two months.
HMV, which first opened 92 years ago, has 22 stores in Scotland including in Buchanan Street, Glasgow, and some of the country's busiest shopping malls.
Half of those will now close, including all five in Edinburgh - Princes Street, the Fort, Gyle Centre, Ocean Terminal, and St James - three in the Glasgow area, at Braehead, Silverburn, and the Fort, along with stores in Dumfries, Falkirk, and Kirkcaldy.
The jobs losses are: Edinburgh Fort – 22; Gyle – 10; Ocean Terminal – 12; Princes Street – 35; St James – 10; Glasgow Fort – 18; Silverburn – 19; Braehead – 27; Dumfries – 8; Falkirk – 11; Kirkcaldy - 9.
Administrator Nick Edwards said the shops had been identified as part of an ongoing review of the company's financial position and the group still hoped to secure a future for the restructured business.
He said: "This step has been taken in order to enhance the prospects of securing the business' future as a going concern.
"We continue to receive strong support from staff and are extremely grateful to them for their commitment during an understandably difficult period."
The group, which currently has 220 UK stores, called in the administrators last month, but hopes of a rescue deal have been raised after restructuring firm Hilco - the group behind HMV Canada - bought the company's debt.
Deloitte said the 66 shops, which employ 930 people, were all loss-making.
The closure plans come after the group axed nearly 190 jobs across its offices and distribution centres last month. Staff then used the company's official Twitter account to announce their own "mass execution" with workers tweeting live about redundancies being made across HMV's offices and distribution centres.
But there was better news for 200 staff at the collapsed group this week after Deloitte offloaded its remaining entertainment venues.
HMV's majority shareholding in G-A-Y Group, which comprises a number of bars and Heaven nightclubs, has been sold to the founder and other shareholder in the business, Jeremy Joseph.
Hilco is thought to be talking to suppliers and HMV's landlords as part of its plans to salvage the group.
Reports suggest Hilco wants to rescue about half of the shops in the UK as it looks to repeat the strategy that has seen it turn around HMV's Canadian arm, which it bought in 2011.Hilco has declined to comment on its plans for the business.
The store closures come amid the high profile collapses of camera chain Jessops and DVD and game rental business Blockbuster last month.
Administrators closed all of Jessops' 187 stores after it collapsed, but sold the business to a group of buyers that includes Dragon's Den star Peter Jones.
The full list of closures is: Ashton-under-Lyne, Ballymena, Barnsley, Bayswater, Belfast Boucher Road, Belfast Forestside, Bexleyheath, Birkenhead, Birmingham Fort, Blackburn, Boston, Bournemouth Castlepoint, Bracknell, Burton-upon-Trent, Camberley, Chesterfield, Coleraine, Craigavon, Croydon Centrale, Derry, Dumfries, Durham, Edinburgh Fort, Edinburgh Gyle Centre, Edinburgh Ocean, Edinburgh Princes Street, Edinburgh St James, Falkirk, Fulham, Glasgow Fort, Glasgow Silverburn, Glasgow Braehead, Huddersfield, Kirkcaldy, Leamington Spa, Leeds White Rose, Lisburn, Loughborough, Luton, Manchester, Moorgate, Newry, Newtonabbey, Orpington, Rochdale, Scunthorpe, South Shields, Speke Park, St Albans, St Helens, Stockton-on-Tees, Tamworth, Teesside Retail Park, Telford, London Trocadero, Wakefield, Walsall, Walton-on-Thames, Wandsworth, Warrington, Watford, Wellingborough, Wigan, Wood Green, Workington, Wrexham.