Both expressions are commonly used, but there is a slight difference in their nuance.
"I am on vacation next week" is more commonly used in American English, where the word "vacation" is often treated as a state or condition. In this case, "on vacation" implies that you are in a state of being on vacation.
"I am on a vacation next week" is also correct and is often used in British English and some other variations of English. In this case, the use of "a vacation" suggests a specific instance of vacation.
Ultimately, both versions are generally understood, and the choice between them may depend on regional preferences or personal style.