It would have also created the world's first government agency to track and punish those who steal music and film on the Internet.
The contested bill had initially passed the lower house of parliament last week. Few lawmakers appeared for Thursday's vote to finalize the measure.
When the vote was held in a near-empty National Assembly, the bill was rejected by a vote of 21-15.
The music and film industry had supported the bill, aimed at boosting industry receipts and cracking down on illegal downloading.
Critics say it will be too tough to apply and encroaches on freedoms.