No, it's not likely to catch fire from a buzz. The cause is usually improper ventilation leading to overheating.
Check the ventilation slots on the back and bottom of the cabinet. They must not be blocked. Move the monitor so there is at least 5 cm (2 inches) of clear space on all sides. Do not place it in a bookcase or cabinet unless there is ample open space behind it. Remove any objects on top of the monitor or covering the vents.
If that didn't work: The noise could be coil whine from the internal power supply, which is generally not dangerous. Ensure the monitor is operating within its specified environment: temperature between 5°C and 35°C (41°F to 95°F) and humidity between 10% and 85% non-condensing.
Heads up: If you see smoke, smell burning, or the performance changes substantially, unplug the power cord immediately and contact qualified service personnel. Do not attempt to repair it yourself.