A security guard was also injured. Police have put the Curtis Culwell Center in Garland on lockdown and told participants in the event not to leave.
Dutch anti-Islamic politician Geert Wilders was attending the conference.
Mr Wilders tweeted that shots had been fired and he had now safely left the building.
It was not clear if the shootings were related to the event.
The event was organised by the American Freedom Defense Initiative, which has campaigned against the building of an Islamic centre near the World Trade Center site in New York.
Sunday`s meeting included a $10,000 prize for a cartoon of the Prophet Muhammad.
Such cartoons are offensive to many Muslims.