Can an employer tell your co-workers what your illness is when you are off on a medical leave?

It probably can.  Unless you have a union/employment contract that prohibits this behavior or it is against company policy to discuss such matters, an at-will employer can divulge this information to co-workers.  That is unless HIPPA privacy rules control.  Under HIPPA (Health Insurance Portability and Accountability Act), certain of a person's medical history is to be kept private.  However, the privacy rule applies only to "covered entities" - health plans, health care clearinghouses, and health care providers.  A covered entity does not include an employer per se.  HIPPA applies to employers only to the extent that they somehow operate in one or more of the foregoing capacities.  In other words, an employer will only deal with covered entities, not actually be one. However, if an employer has any kind of health clinic operations available to employees, or provides a self-insured health plan for employees, or acts as the intermediary between its employees and health care providers, it will find itself handling the kind of personal history information that is protected by the HIPAA privacy rule.  Therefore, the degree of compliance required of an employer will depend on how involved it is in administering its health plans and on how it funds health benefits.

Note:  The HIPAA privacy rule establishes a national minimum standard. If a state law provides greater privacy protections, the state law must be observed.

Bottom line,  Speak to your HR department or consult directly with an employment law attorney in your area as to your rights, and whether or not they have been violated.