Vandals have damaged and destroyed rare cacti inside Melbourne's Royal Botanic Gardens.

Cacti in the Arid Garden were hacked with a sharp implement, such as a machete or axe, according to the garden's staff.

About 80 per cent of the columnar cacti and succulents were attacked, staff said.

Many of the plants were more than 30 years old and the collection contained some rare and threatened species.

The garden's chief executive, Tim Entwisle, says the damage had shocked staff and visitors.

He says it is difficult to comprehend.

"Someone's come in overnight and they've just hacked away at some of the biggest cacti in our collection - the tall, column like ones. Just broken them off, left them there," he said.

Victoria Police are investigating the matter, while the garden is now temporarily closed.

The vandals destroyed the cacti in the Arid Garden overnight on Tuesday. ( Supplied )

Mr Entwisle said after damaging the cacti, the vandals fled.

"It's just a horrible sight to see," he added.

It would take decades for any replacements to reach the maturity of the plants that were destroyed, Mr Entwisle said.

The Arid Garden was set up to display a range of plants species with adaptations for survival under dry conditions.