Short answer. Only on strict conditions. Article 284 allows dismissal for disease where continued employment is prohibited by law or is prejudicial to your health as well as your co-workers', and only if separation pay is paid. A treatable case will rarely meet that standard.
What the law says
An employer may terminate the services of an employee who has been found to be suffering from any disease and whose continued employment is prohibited by law or is prejudicial to his health as well as to the health of his co-employees
Labor Code, Article 284 — Disease As A Ground. Read the full provision →
The test is about continued employment, not the diagnosis
Read what the article actually asks. Not whether you are ill, but whether your continued employment is prohibited by law or is prejudicial to your health as well as to your co-employees'. Those three words do real work: harm to you alone is not enough, and neither is risk to others alone. Nor is the employer's inconvenience — absences for treatment, reduced output, a client's discomfort — any part of the test. An employer who cannot say which of the two limbs your case falls under has not engaged with the provision at all.
Curability is where these dismissals usually fail
The implementing rules require a certification from a competent public health authority that the disease cannot be cured within six months even with proper medical treatment. That is a deliberately high bar, and it is not met by the opinion of the company clinic or a doctor the employer sent you to. Tuberculosis is treatable on a standard course, and an employee who is under treatment and compliant with it is ordinarily heading towards fitness rather than away from it. If no such certification exists, ask for it in writing before you accept that the ground is made out.
Separation pay is a condition of the power, not its consequence
The authority to terminate is granted only provided the employee is paid separation pay of at least one month's salary, or half a month's salary for every year of service, whichever is greater, a fraction of at least six months counting as a whole year. So payment is not something that follows a valid dismissal; it is part of what makes the dismissal available in the first place. An employer who separates you for illness and pays nothing has not exercised this ground, whatever the medical position turns out to be.
Protect the medical record, and mind the substitutes
Keep everything from your own treating physician: the diagnosis, the treatment plan, the record of compliance, and any clearance saying you are fit to work or fit with limitations. Ask in writing for a copy of whatever certification the employer is relying on. Note whether you were offered lighter duties or a temporary reassignment, since a workable alternative undercuts the claim that continued employment is prejudicial. And be careful if you are urged to resign, take indefinite leave, or sign a release instead — a resignation costs you the entitlement this article guarantees.