Is there any violation if a supervisor insists on knowing what is wrong with an employee who has a medical condition/disability, and the employee feels awkward, especially when the subject is introduced in the company of another employee? She believes she should know what is wrong because she doesn't know what to tell people? Isn't it an invasion of privacy?

It is an invasion of privacy if the questions are asked in front of another employee. It is also poor leadership and bad management. If and only if, your medical condition directly affects your job then it is important to disclose that but in absolute privacy with an advocate, such as a human resources person or your own legal counsel; present. The reason your employer needs to know is that if a third party is "injured" financially, physically or in any other way as a result of your medical condition - your employer is liable and could be sued for damages. So it's important that (a) the disclosure is done in private with an independent third person present and (b) that your boss not tell ANYONE else in the organisation about the medical condition. OK?

Invasion of privac yes, if she forces the employee to tell them under threat of punishment it is wrong, esp in front of another employee.
And it is not their place of a supervisor to tell anyone anything other than management. The answer to the supervisor is, we can discuss it in private, or I have given the reason for my absent to HR already

I have been out of work for several weeks due to a chronic medical condition. At a staff meeting on 6/19/08 it was announced to all employees at the weekly staff meeting that I would not be coming back. The announcer proceeded to discuss my medical condition in some detail and proceeded to state that when she made an unannounced visit to my home, I was embarrassed because my house was a mess. I received several calls from staff members who were surprised that I was, indeed, not returning to work. When I called my supervisor, she said, "I was wrong. I should have let you know first." Do I have any recourse? Thanks

I'm not legally qualified but if you have notes made at the time this happened, I would definitely seek a legal opinion about that as I don't think they can just tell everyone about your medical condition without express written permission from you. But I am happy to be corrected. But I would call an employment lawyer.