The scratches were discovered after the double-decker plane, the world's biggest passenger aircraft, arrived in Frankfurt on Sunday from New York, SIA said in a statement.
There were 126 passengers and 26 crew onboard.
"The aircraft was subsequently grounded for checks and passengers were either transferred to other airlines or accommodated in hotels," the statement said.
"Following inspections by engineering teams in Frankfurt, it was determined that the scratches posed no safety issue and the aircraft was cleared for departure."
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SIA said the cause of the scratches has yet to be established.
"Our engineers are currently performing further checks on the aircraft, and it will resume service once cleared," the airline said.
A source close to Airbus told AFP in Paris today that the scratches were probably caused by a "defrosting system" at the John F Kennedy International Airport in New York.
Experts say the defrosting equipment is used to remove and prevent the build-up of ice on the plane's outer surface, especially on the wings and fuselage, by spraying chemicals using high-pressure water jets.
The incident on Sunday was the second for SIA in less than a month involving an Airbus 380.
On January 6, an SIA A380 en route from London to Singapore lost cabin pressure, forcing the pilot to make an emergency landing in the Azerbaijan capital of Baku.
Oxygen masks were activated during the emergency procedure which some passengers described as "frightening".
The stranded 467 passengers and 27 crew on board were flown back to Singapore with a replacement aircraft.