Capability Scotland said it had decided that the 2.6 million pedestrian bridge, which would have linked Perth with Scone, was "not in the best interests" of disabled adults living at its care home in Isla Road, Perth.
Perth and Kinross Council's plans to sacrifice the green on the signature 15th hole of the city's North Inch Golf Course to site one of the buttresses for the bridge had been met with outrage.
"The hole at the publicly-owned course has been listed as one of the top 100 golf holes in the UK.
Mr Morris' great-great-grandson Melvyn Hunter Morrow had condemned the council's plan as "bound to destroy" one of his ancestor's design masterpieces.
The announcement that the Connect2 Bridge was now on hold was made by Perth and Kinross Council, after it was told by Capability Scotland that it no longer wanted the development on its land.
Capability Scotland chief executive Alan Dickson confirmed it had taken the "difficult" decision of opposing the project, but residents and golfers welcomed the charity's intervention.
Jack McLeish, chairman of the North Inch Users' Group, said: "The decision by Capability Scotland to withdraw the use of their land at Upper Springlands for the Connect2 Bridge will be warmly welcomed by Perth golfers.
"We very much hope that this will end the council's plans for this crossing point, and the layout of the historic old North Inch golf course will be preserved for the future."
He added: "We are not against the bridge being built - although I feel it is as gross waste of public money - all we asked was that it should not be built on top of the golf course."
Pauline McGarrie, who lives on Isla Road, said: "I just have to express my absolute delight at the news that the Connect2 bridge will probably not go ahead.
"It is the best Christmas present anyone could have given us. I will be raising a glass on New Years' Day to what I hope is the end of what has been a very worrying time."
The North Inch course, which is home to the first golf society in the world to gain Royal patronage, was partly designed by Old Tom Morris, a four-time winner of golf's Open Championship, who was also responsible for the design of Carnoustie, Muirfield and the Jubilee Course at St Andrews.
Mr Hunter Morrow said: "It is as important to Perth as the Stone of Destiny is to Scone and we shouldn't eradicate or remove what is left of Old Tom's work."
Council leader Ian Miller said Capability Scotland's withdrawal of permission would have "serious implications" for the controversial pedestrian and cycle bridge.
He said: "It doesn't leave us with a lot of options."
The council has written to Capability Scotland urging it to reconsider.
Murdo Fraser, MSP for Mid Scotland and Fife, said: "There will be relief for supporters of the North Inch Golf Course if the bridge project is not now proceeding, as they felt it was not acceptable that this historic golf course was going to be damaged and permanently altered as a result of its construction."
The bridge would have run through the centre of the 15th green, requiring it to be relocated northwards by 30 metres.