Airbus sent a letter to state-owned Emirates, which has ordered 58 of the aircraft, informing it of possible delays in its "wave 2" deliveries, airline President Tim Clark told Reuters by telephone in Dubai.
This would apply to A380s being delivered to the carrier from April next year, Clark said.
"It's very serious," said Clark, whose first delivery due this year is already almost two years behind schedule. "This will do us serious damage." Profit growth would be hurt, he said.
Emirates expects to receive five A380s before the end of March and another 12 in the year to March 31, 2010.
"We'll know in two to three weeks if it's ok or not," Clark said. Airbus did not explain why the deliveries could be delayed, Clark said. Airbus declined to comment.
Deliveries have fallen behind schedule after a series of industrial mishaps since 2005, and the reputation of parent EADS
is seen at stake as it strives to deliver 13 planes this year.
Shares of EADS were down as much as 1.4 percent on Tuesday by 0958 GMT.
"I am currently conducting a major review of the (production) ramp-up plan," Airbus Chief Executive Tom Enders told reporters in the United Arab Emirates last week.
"We are conducting a review right now, (it) might well be that we achieve that," he said in response to a question on whether Airbus would achieve its delivery targets.
Airbus' targets called for 13 deliveries of the 525-seat, double-decker passenger plane in 2008 and 25 in 2009.
The $300 million A380 went into service last year with Singapore Airlines but is heavily bankrolled by Emirates.
Europe's biggest single industrial project was thrown into upheaval in 2006 when A380 sections reached the French assembly plant with small wiring flaws that caused production to halt.
Airbus blamed the failure of German and French plants to use the same design software and was forced to start assembling the first 25 planes by threading the 500 km of wiring through each aircraft manually, pushing deliveries back on average 2 years.