Swansea Council said its parks team is working carefully to remove the tree, which was uprooted by high winds and is now lying across a section of the cemetery.
Smaller branches have already been cut away to reduce the weight of the trunk, but a crane is due on site to lift the main stem clear without causing further damage.
Cllr Cyril Anderson, Cabinet Member for Community, said:
“At the moment, the fallen tree is sitting across a number of headstones and is fairly stable. We are taking our time with the removal, so further damage is not caused. This means working methodically to avoid uncontrolled movement of the tree stem as well as consideration for the safety of our park operatives when working with such a large structure.
“We understand how distressing this may be for families, and we want to reassure them that we’re doing all we can. Once the tree has been removed we will be able to undertake a full assessment of any damage that has been caused and will contact those families affected by this incident.”
The cemetery remains open to the public, but visitors are being asked to avoid the affected area until the tree has been lifted clear.
