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The plane, which landed safely in Colombo, was 320 nautical miles east of Colombo's Bandaranaike International airport when pilots made a distress call, airport's chief air navigation services officer Crishanthi Tissera said.
"The pilots said May Day, May Day and we activated all our emergency services and brought the aircraft to a safe landing," Tissera told reporters.
She said the pilots reported smoke in the cockpit but later the "full emergency" was downgraded to an "urgency".
There was no fire seen as the plane landed 39 minutes after the first distress call. All 471 passengers, including six children and the 30-member crew disembarked safely.
"Emirates flight EK413 from Sydney to Dubai...was diverted to Colombo due to a technical fault," the airline said in a statement without giving details about the nature of the problem.
"The aircraft landed safely at the Bandaranaike International Airport and passengers were transferred to other Emirates flights," the Emirates statement said and apologised to passengers for any inconvenience.
Fire fighting crew and emergency units had been placed on stand by.
The Airbus A380 is a double-deck, wide-body, four-engine jet airliner manufactured by Airbus. It is the world's largest passenger airliner and the airports at which it operates have upgraded facilities to accommodate it.
Emirates carried out its first A380 landing in Colombo in 2012 but the airport has yet to be upgraded to handle the plane.
PTI
Comment: Yet another incident of 'smoke in the cockpit'! Other recent reports include: "burning electrical or smoke", "odor of fumes" in cabins and smoke filled cockpits - forcing emergency landings. What is going on 'up in the air'?
See also: Sott Exclusive: Mayhem and Maydays in May skies: Aircraft crashes,accidents, glitches, mishaps and near misses