A woman applying for her driving licence received a letter from the DVLA addressed to "multiple sclerosis Caron Garrod".
Ms Garrod from Goring-by-Sea, West Sussex, had told agency staff about her medical condition when reporting that she had not received mail from them.
She said of the blunder: "I will tell anyone who asks about my condition but this is just so offensive."
The agency has apologised and promised an urgent investigation.
The DVLA letter from its Drivers Medical Group on 24 November was sent in response to a telephone call Ms Garrod had made to the agency a week before.
She said she had "many feelings about the letter... first anger, then I was horrified when I realised it had gone all the way through the postal system".
She said she was shocked the agency could be so "insensitive and negligent" to allow it to happen.
She added: "I'm quite a robust person mentally but there are many people with medical conditions who would be severely affected by a situation like this."
The Office of the Information Commissioner said medical information is classed as "sensitive personal data" under the Data Protection Act 1998.
This means there are stricter rules concerning its processing and security.
It said: "Organisations have a legal duty to ensure that they protect people's personal information, particularly when it is sensitive data such as medical information."
A DVLA spokesperson said: "While mistakes like this are very rare, we are extremely sorry for any distress caused.
"We take the security of our data very seriously and we are investigating this as a matter of urgency to ensure lessons are learned."