Short answer. Only if your continued employment is prohibited by law. Article 284 gives two routes, and the second requires that staying on be prejudicial to your health as well as to the health of your co-employees. Where nobody else is at risk, that second route is not made out.
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 →
Having a disease is not the ground
The article does not permit dismissal because an employee is ill. It permits dismissal where an employee has been found to be suffering from a disease and one of two further conditions holds. Illness alone, even serious or prolonged illness, does not satisfy it. That is the assumption most readers arrive with and it is the wrong starting point: the question is never simply how sick you are, but whether your continued employment falls within one of the two situations the provision describes.
The two routes, and what separates them
The first is that continued employment is prohibited by law. That is an external prohibition — a legal rule that bars someone in your condition from doing that work — and it does not depend on risk to anyone else. It either exists or it does not, and the employer should be able to identify it. The second is that continued employment is prejudicial to his health as well as to the health of his co-employees. The words as well as join the two, so on the face of the provision a risk confined to you alone does not complete this limb.
Found to be suffering
The phrase has been found to be suffering carries weight of its own. It points to a finding about your condition rather than an employer's impression of it, and it puts the medical question ahead of the managerial one. In practice that means the employer's own view that you look unwell, that you have used a great deal of leave, or that colleagues are uneasy, is not a finding. Ask what your condition was determined to be, by whom, and on what basis — an employer relying on this ground should be able to answer.
If the ground does apply, the payment is a condition
Where the article is satisfied, it does not simply permit the dismissal. The employer may terminate provided that separation pay is paid, at a minimum of one month's salary or half a month for every year of service, whichever is greater. So a termination on this ground with nothing paid is defective on its own terms. Keep the notice you were given, any medical documents you were asked to submit or were shown, and your dated record of service. Those are the three things a lawyer needs to assess both the ground and the amount.