Witnesses reported the blast after hearing a loud noise, and images of flames and smoke were shared on social media.
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Security sources said the 12 injured people were taken to hospital for treatment.
Army spokesperson Tamer el-Refai said on Twitter an "increase in heat" caused the explosion, which took place at a company specialising in "chemical industries" in an area controlled by the army.
The area was cordoned off by a strong police presence, according to an AFP correspondent on site, who said fire engines and emergency vehicles were sent to fight the flames and help the wounded.
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The Department of Civil Aviation denied that the explosion took place inside the airport, as indicated by some witnesses.
"Air traffic continues," Ministry spokesperson Bassem Abdel Karim said in a statement.
"Departing and arriving flights are not affected," he added.
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