The woman was working at Clydebank's Golden Jubilee Hospital treating a patient with the highly infectious disease before she became ill.
A spokesman for the Health and Safety Executive said it is investigating the case which was reported to them last February.
Inspectors are working with hospital staff in a bid to determine the circumstances in which the disease was contracted.
If the HSE find that proper procedures and training were not carried out they could lodge a report with procurator fiscal.
One potential line of inquiry is whether the hospital supplied adequate face masks.
The Golden Jubilee is a major centre for heart and lung services and is run by the NHS National Waiting Times Centre Board.
It is a 'flagship hospital' for reducing waiting times in key elective specialities.
A spokeswoman for the HSE told the Evening Times it had launched its investigation after it was made aware of the case under the Reporting of Injuries, Diseases and Dangerous Occurrences Regulations 1995.
A HSE spokeswoman said: "I can confirm that there is an ongoing investigation at the Golden Jubilee.
"This relates to a case of an employee who contracted tuberculosis.
"This was reported to us under the guidelines."
The HSE said the investigation is ongoing.
Jennifer McCarey, Unison area organiser, said the union was aware of the investigation but not directly involved in the case, which she said related to a female employee.
She said: "I am very concerned about this and expect rigorous examination of the processes which have failed – if TB was contracted by a member of staff.
"Cases of health care employees contracting diseases at work are rare occurrence in the health service.
"Protecting staff should be the number one priority for any employer.
"If all the existing systems and procedures are put in place and appropriate training is carried out then staff should be safe.
"When a member of staff falls ill, it is because this system has failed and they have not been protected sufficiently."
She added: "This is by no means an acceptable hazard of the job.
"Health care staff should be able to go to work with the confidence that they are protected no matter who they work with and how ill they are."
Lindsey Ferries, director of human resources at the hospital, said: "We can confirm that the Golden Jubilee Hospital is working with the Health and Safety Executive while they carry out an investigation and are currently awaiting the outcome of this.
"Valuing all of our staff and providing a safe and healthy workplace is one of our top priorities."
TUBERCULOSIS (TB) is a serious bacterial infection spread through inhaling tiny droplets from the coughs or sneezes of an infected person.
TB mainly affects the lungs but can affect any part of the body, including the bones, nervous system and kidneys. It can also lead to meningitis.
Before antibiotics, TB was a major problem in the UK.
The condition is now much less common but in the last 20 years cases have gradually increased.
According to Health Protection Scotland, there are around nine cases per 100,000 people in Scotland.
TB is given as the underlying cause of death in around 30 to 40 Scottish people every year.
Rising rates of TB in other parts of the world – sub-Saharan Africa, Asia and South America – have caused the disease to be declared a global emergency by the World Health Organisation.
Children in the UK are protected from the disease via the BCG vaccination.