The service from London to the city-state landed safely without any injuries to the 467 passengers and 27 crew members on board, a Singapore Airlines spokesman said.
"Oxygen masks were deployed and the aircraft landed uneventfully at Baku airport at 01:03 (2103 GMT yesterday)," he told AFP by email.
"We are seeking clearance from local authorities to transfer affected customers to a hotel until a replacement aircraft arrives from Singapore."
In a Facebook post, passenger Matthew G Johnson said a "loud air noise was heard from the door five rows in front" shortly after take-off from Heathrow Airport in London.
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A few hours later, oxygen masks were deployed and the aircraft began an emergency descent over Afghanistan after the cabin began losing pressure, he said.
Singapore Airlines has a fleet of 19 Airbus A380s, with five others on order, according to its website.
The planes are used for flights from Singapore to various destinations including Frankfurt, Hong Kong, London and Los Angeles.