Yes, you need a Schengen visa.
I sense from the way that you've written your question that you've misunderstood what Schengen is. "Schengen visa" is like, say, "U.S. Visa", not like "tourist visa". The countries of the Schengen zone have decided that they will issue visas collectively, rather than each country issuing its own visas. There is no longer any such thing as an Austrian visa, Slovak visa or Czech visa: anybody travelling to any of those countries (and 23 others) who requires a visa requires a Schengen visa. (Analogously, there's no such thing as a Massachusetts visa: anybody who wants to travel there and who needs a visa needs to get a U.S. visa.)