Princes Golf Course, at Braid Hills, was found badly damaged on Saturday morning.
The vandals, described as "mindless" by one golfer, drove deep grooves and several figures of eight at the seventh green at the nine-hole course.
The course, which was set up specifically for juniors and people just taking up the game, will now take up to nine weeks to repair.
A spokesman for Edinburgh Leisure said: "We believe that some form of 4x4 vehicle was driven on to the seventh green. There is extensive damage from tyre tracks on the green, which will require it to be returfed.
"Unfortunately, this repair work could take up to a maximum of two months to complete, during which time the green will be unplayable. However, golfers will still be able to play a full round of golf at the Princes as a temporary green will be put in place."
A regular golfer, who used the course three or four times per week, said: "This is a shocking incident and it isn't the first of its kind. A couple of years ago some youths drove a motorbike on the green and did exactly the same sort of thing."
The 75-year-old, who did not want to be named, added: "It's a real shame because a lot of retired people and beginners use the course. It was a wonderful green which was kept to the standard of a private golf club, and now it has been mindlessly destroyed."
He added that although there was still the option of playing at the 18-hole Braid Hills course until the green repairs were done, some would find it hard going.
He added: "The 18-hole course is arduous and not suitable for those with a high handicap."
The vandalism is the latest in a series of attacks on golf clubs in the Lothians which have been reported in recent months, causing more than 100,000 in damages to equipment and turf.
In one of the worst incidents, more than 55,000 worth of fire damage was caused to vehicles and buildings at Carrick Knowe Golf Course.
In July, the Evening News also reported how damage was caused at Torphin Hill Golf Club when joyriders used four golf buggies to smash their way through a fence on to the course, damaging the buggies and the greens.
Police are appealing for information on the latest incident.
A spokesman said: "Police are investigating after a green was vandalised at Princes Golf Course. The vandalism is believed to have happened overnight from Friday into Saturday. Inquiries are ongoing, and anyone who has any information regarding this incident should contact police."