The American Freedom Defense Initiative organised the event featuring far-right populist Dutch politician Geert Wilders, who has been outspoken against Muslims.
"#garlandshooting cop shot - two suspects dead, awaiting bomb squad for possible explosives at our free speech event #sharia," political activist and AFDI co-founder Pamela Geller wrote on Twitter.
SWAT officials told ABC television news affiliate WFAA that the two male suspects drove up and opened fire on the Curtis Culwell Center in Garland, near Dallas, which was hosting the exhibit and the Prophet cartoon contest billed as a "free speech" event.
2 male suspects drove up and opened fire on the Curtis Culwell Center
The police officer was shot in the leg and was rushed to hospital, where he was expected to recover, according to local CBS news affiliate DFW. Police were searching the area for a vehicle containing explosives.
A local police-themed blog that posts information coming from public scanner radio said a suspect had been spotted at a nearby store with a hand grenade, and that the expo center and surrounding businesses were evacuated.
"There are multiple reports that two explosives have been placed in the area of Curtis Caldwell Center," the Rowlett/Sachse Scanner wrote on its Facebook page. AFDI offered a USD 10,000 prize for the winner of the cartoon contest.