The request was made Scottish Golf in a statement issued following Prime Minister Boris Johnson’s television address to the nation about the latest measures to combat the coronavirus pandemic.
The governing body said: "While golf is an outdoor sport that allows players to exercise in the fresh air, the message to all of us is clear, we must stay home and play our part in containing the spread of Covid-19.
"With this in mind, Scottish Golf asks that all golfers in Scotland refrain from golfing until further notice.
"We understand that this advice will have a significant impact on golf clubs across the country and we will continue to consult with industry partners to provide clubs with all information and support possible during this time of deep uncertainty.
"We know that these decisions are difficult ones to make, but right now, it is our shared responsibility to prioritise the health of our local communities by working together to follow the Government guidelines.
"In doing so, this will ensure that we get the opportunity to play the game that we all love as soon as it is safe to do so."
A raft of Scottish clubs responded to the Prime Minister's plea for people to stay at home by announcing course closures.
They included Gullane, Bruntsfield Links, Turnhouse, Kilspindie, Luffness, Musselburgh and Mortonhall while Kingsfield Golf Centre at Linlithgow has also been closed for the time being.
Meanwhile, south of the Border, England Golf went a step further by issuing a statement saying that all golf clubs, courses and facilities "must now close".
"Keeping golf courses open is simply no longer compatible with the updated policy of government which is designed to save lives in a time of national emergency," said the governing body in England in a statement.
"The health and wellbeing of the nation is the only consideration that matters at this moment in our history.
"These are incredibly testing times for the country. The golf industry cannot be shielded from the economic and social ramifications caused by this temporary shutdown of normal life."