Formal and slightly old-fashioned. It appears more often in serious writing than in everyday speech, where disapproval is more common. The noun often takes of before the person, behaviour, or plan being judged.
常見錯誤
Her disapprobation about the rude email was obvious.
Her disapprobation of the rude email was obvious.
The noun normally takes 'of' before the person or thing being judged.
I felt disapprobation for the soup because it was cold.
I disliked the soup because it was cold.
disapprobation is a formal word for moral or social disapproval, not ordinary dislike.