Health bosses said urgent care and cancer treatment is being prioritised due to a "sustained and significant rise" in patients requiring treatment for Covid and non-Covid related medical conditions.
Community transmission remains high in Fife.
In the last week, 3,129 positive cases have been reported in the Kingdom - the 13th highest rate of any local authority in Scotland.
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Margo McGurk, deputy chief executive of NHS Fife, said: “The pressure on healthcare services in Fife at present is unlike anything we have experienced during our response to the pandemic.
"Current projections are suggesting that this unprecedent demand will continue and increase still further.
"It was therefore vital that we had to act now and take the difficult decision to postpone routine procedures to protect our urgent care and cancer services."
Ms McGurk added that the decision was "not taken lightly" but was made in the name of patient safety.
"Postponing some clinical services will enable staff working in these areas to support their colleagues in emergency care, trauma, and cancer services to ensure those who are most unwell receive the vital care they need," she said.
“We know that this decision will have a direct impact on our patients, some of whom will have already waited a considerable period of time for treatment, and we sincerely apologise for the additional anxiety this will cause.
"Our hope is that this postponement will be brief, and we can resume any services stepped down as soon as it is safe to do so."
Presentations to the emergency department at the Victoria Hospital over the summer months have far exceeded expectations - thought by doctors to be a combination of conditions exacerbated by coronavirus and people staying away from hospital during the pandemic to avoid overwhelming the health service at the virus' peak.
A&E has recorded five of its six highest daily attendances since records began in recent weeks.
Patients will be contacted directly to advise of any changes to their appointments, and visiting restrictions will be limited to one person per patient.
In a direct plea to the public, Ms McGurk has asked locals to be mindful of how they are using the NHS to avoid overwhelming it further.
“Our ask of the people of Fife is to continue to do their bit to support healthcare staff and services," she said.
"We need to ask the public to use our emergency services, especially our accident and emergency department appropriately.
"The public should also continue to play their part in helping to reduce Covid rates in our communities, and in turn reduce the number of people requiring treatment for the virus in our hospitals.
“That means getting fully vaccinated against Covid, and we have a range of drop-in clinics available across the Kingdom. It is also equally important that anyone with even very mild symptoms of Covid isolates immediately and books a test at one of the many sites in Fife.
“Taking these steps will not only reduce community transmission and result in fewer people becoming unwell, but it will also reduce the number of those requiring care in our hospitals and help alleviate the significant strain on services.”