Ahmed Dogan, 58, the long-time leader of the Movement for Rights and Freedoms (MRF) escaped unscathed, and it was not immediately clear why the attacker had targeted him.
The incident happened at a party congress in downtown Sofia.
Television footage showed the man jumping out of the audience and interrupting a speech by Dogan, who has led the party for almost a quarter of a century. Security guards were seen beating and kicking the attacker.
"Ahmed Dogan is in good health. Everything is under control," MRF official Ceyhan Ibryamov told journalists.
Police said they had arrested a 25-year-old man from the Black Sea town of Burgas who was also carrying two knives.
The liberal MRF party represents ethnic Turks and other Muslims who make up about 12% of Bulgaria's 7.3 million-strong population.