Do you need a master degree to pursue a career in the music industry

Not required. Real world experience trumps all. But a masters doesn't hurt if your are focused on a specific goal, or even a law degree of you are serious about negotiating music business contracts and doing management.

Silviya D. "I am a vocalist (mainly trained in pop & Jazz)"

Now the answer is easy. A masters degree is nice - BUT if talent isn't there the degree will be fruitless. I'll use Luther Vandross as an example. He never completed college and had one of the greatest careers you can think of solely by singing and compossing his way to the top.

All great singers have natural ability and can use their voice to fit a musical composition. Whether it be for backing vocals, lead vocals or in some cases a ghost vocal (that other singers - rappers use for guidance and tempo, then gets erased before the final mix)

Examples of Luther singing:
Juicyfruit gum commercial: https://www.youtube.com/watch?v=35AJsxRSQ7Y

1976 Funky Music (Is a Part Of Me) - Luther Vandross https://www.youtube.com/watch?v=2qEDfcgqzpM

1989 Luther Vandross - Here and Now https://www.youtube.com/watch?v=vLH1y8Kfv94

Listen to these examples, you can see how he kept growing to fit the musical styles of each performance.

So, in answer to your original question, "Do you need a master degree to pursue a career in the music industry?" No. You need talent and a great amount of perseverance to succeed.

What is your specific field of study? Engineering, instrument, composing, etcetera...