Following a judicial review, Lord Jones said ministers reached their decision on SSE's Stronelairg project "in breach of environmental obligations".
Landscape charity the John Muir Trust sought the review after the wind farm was given planning consent last year.
The trust said the turbines would "destroy the character" of wild land.
Stuart Brooks, the John Muir Trust's chief executive, said the charity was "delighted" with the review's result. The Mountaineering Council of Scotland and National Trust for Scotland have also welcomed the judicial review.
SSE said it was "disappointed".
The court heard that Scottish Natural Heritage had objected in principle to the wind farm's proposed site.
Lord Jones said: "If the ministers did take into consideration SNH's objection in principle to any wind farm development at Stronelairg, they have given no reason for rejecting it, and the decision is defective on that account."
The public was also denied an opportunity to comment on a revised planning application for the proposed wind farm, the judge said.
He said the government's decision to give consent should be set aside.
Energy Minister Fergus Ewing granted permission for SSE Renewables' project in July last year.
It was said at that time the wind farm could generate enough electricity to power 114,000 homes.
The operators also said it would bring Â£30m-worth of benefits to the region.
However, the John Muir Trust said the development would "destroy the character" of an area of wild land in the Monadhliath Mountains.
It lodged a petition to the Court of Session asking for a judicial review of his decision.
SSE had sought permission for up to 83 turbines at Stronelairg near its Glendoe hydro electric scheme above Fort Augustus.
However, in April 2013, Highland councillors voted 11 to three in favour of raising no objection on the understanding the project was reduced to 67 turbines.
Following the judicial review, Mr Brooks said: "This is great news for all those who love Scotland's wild land and wish to see it protected.
"A financial appeal brought a tremendous level of support from over a thousand well-wishers, allowing the trust to proceed.
"Lord Jones has now decided the trust's court action was well-founded."
A spokesperson for SSE said: "We are disappointed with the result of the judicial review of the consent decision for Stronelairg wind farm.
"We will now review the judgement in detail and consider our options accordingly."

He has played 12 games since arriving in October on non-contract terms.
"It's down to the club to put something on the table in January and we can take it from there," 29-year-old Gerrard told BBC Radio Shropshire.
"If somebody wants a player badly enough, those funds can miraculously appear from out of the blue."
The cousin of former Liverpool and England skipper Steven Gerrard, he was released by Huddersfield Town in the summer, having made only 10 appearances in 2014-15.
He is grateful for the opportunity given to him by Town boss Micky Mellon, who has warned that he will not spend money the club does not have.
"It's the first time I've strung a consecutive amount of games together in about a year and a bit," said Gerrard. "I'm just concentrating on each and every 90 minutes that I can get under my belt.
"For a player who has played whole seasons, last year was a bitter blow to my career. But it's done now. I'll be glad to see the back of 2015, and look forward to a promising 2016. I'm here to play.
"I'm here to do what I can for the team and help them get to a nice solid base. I can see myself staying here, but obviously there's a lot to be talked about and figures to be spoken about before that can happen."
A judge at the Court of Session has said the Scottish government's decision to approve a 67-turbine wind farm near Fort Augustus was "defective".
[NEXT_CONCEPT]
Shrewsbury Town defender Anthony Gerrard hopes that talks can take place next month with a view to him signing a full-time contract at the club.