An investigation was launched after masonry fell during a funeral.
No-one was injured in the incident, but a Cardiff council environmental health officer went to the cathedral and inspected the area.
A council spokesman said: "The officer visited immediately and we are satisfied with the actions that are being taken to ensure public safety.
"Debris isn't falling from the outside of the building to endanger the public, but we will continue to monitor the situation."
The Dean of Llandaff, the Very Reverend Gerwyn Huw Capon, said it came as one of the challenges of running a fifth century building.
He said: "Like any custodian of a public building we have people such as architects and masons in hand to check for problems when they occur.
"We are always having work done, investigations and repairs to stonework.
"The architect did notice two small areas of stone with hairline cracks in a non structural pillar towards the east end of the building.
"These need a different type of access arrangement, so an access hoist is being brought into the cathedral on Friday to enable this to happen.
"These areas have been cordoned off until Friday."
Hairline cracks have been found in a pillar in Cardiff's Llandaff Cathedral.