The announcement comes despite the track having a deal to stage races until 2006.
Speaking in Austria's Kronen Zeitung newspaper, Ecclestone said: "We'll be racing for the last time in Spielberg on 18 May this year - then it's over.
"We had a contract with Spielberg until 2006, but with an exit clause that's now come into effect.
"Austria's health minister is the one to blame because he agreed to bringing forward the ban on tobacco advertising."
The introduction of the ban on tobacco advertising has been brought forward to the end of 2005 from the end of 2006. A similar decision prompted the FIA to drop Belgium's Spa track from the 2003 calendar.
Added Ecclestone: "In 2004, we're racing in Shanghai and Bahrain, 2005 in Istanbul, then in Russia.
"It's possible that we then only have five or six races in central Europe."
The Austrian Formula One Grand Prix in Spielberg has become the latest victim of a government decision to bring forward tobacco sponsorship bans, with Bernie Ecclestone confirming the 2003 race would be its last.
