The road allows thousands of cars a day to access the main dual carriageway into the east of Edinburgh.
Drivers are incensed that they are being forced to take a detour of up to four miles, taking as long as 15 minutes in the rush hour, for the benefit of one family.
The closure, which came in to effect this week, affects around one thousand familes in the nearby suburb of Stoneybank - who are usually only seconds away from the city bypass.
The decision by East Lothian Council has been branded “ridiculous”.
The owners built a detached house with separate garage, four bedrooms and large garden.
The land alone cost £130,000 and, once completed, the property in Stoneybank, Musselburgh is likely to be worth well in excess of £250,000.
Sewage and gas work is needed to finish the property meaning part of the B6415 will have to be dug up.
East Lothian Council decided to shut the road completely on Monday and it will not reopen until next Thursday.
The council stated: “This will enable our building control to issue a habitation certificate and permit a young family to spend Christmas in their new home.”
Neighbours, most of whom live a few hundred metres from the junction with the A1, were outraged and took to social media to protest.
Jane Grieve wrote: “Eh? Is it the royal family?”
Emma Jane Wyatt Bannerman wrote: “How dare they? Shutting a major road is wrong. Did you ask the opinion of others that live nearby? No you didn’t. So wrong.”
And Jacqueline Higgins said: “You could have built a housing estate quicker and without road closures. Hope they have a Merry Christmas.”
Fraser Pike said: “I think everyone should send them a bill for their extra petrol, cheeky blighters.”
Speaking at his home a few minutes’ walk from the newbuild, Raymond McCabe, 74, said: “It’s a bit strange that the reason the road’s getting closed is so the family can get in for Christmas.
“From 8am in the morning to about 9am that road can be completely gridlocked - over 7,000 commuters each day. I can’t understand why the whole road is being closed.”
The Denholm family, who currently live in nearby Port Seton, did not answer the phone or respond to messages left at their home.
But a man at the site of the new property, who said he was a family member but declined to give his name, said: “People are making out as if the family are rich and that they know people. It’s the exact opposite of that. This work should have been done months ago.”
A spokesman for East Lothian Council said: “Road closure to enable new infrastructure and access for utilities is not uncommon and we take into account the needs of the builder/homeowner and road users when making our decision. In this case the safest and most efficient solution was to close the road temporarily.
“The depth of excavation to access main pipes is almost three metres, which means the road needs to be closed for this work to be carried out.
“If it was done in two stages, that is closing one lane and allowing cars through on a single track, this would actually last longer, approximately five to six weeks. So closing and doing this in a concentrated manner reduces the time to ten days.”