"If a major airline that invited us... to join the Oneworld is today restricting us from operating into that country... then I don't need to be part of this alliance," he told the BBC.
"I can do it alone," said Mr Al Baker.
Doug Parker, the chief executive of American Airlines, said they did not have a dispute with other airlines.
Rather, Mr Parker said it was for the authorities in Washington to act on this issue.
"We have a view that our US government should enforce its trade policies," he said.
The Oneworld alliance is an agreement between 15 airlines to share resources, and includes Qatar Airways and American Airlines.
"We didn't come begging them [American Airlines] to be in the alliance. we were invited by them," said Mr Al-Baker at the  International Air Transport Association's (IATA) annual meeting in Miami.
"If they don't honour the commitment of an alliance then we don't want to be in this alliance.
"And there are many other American carriers that would like to do business with us so actually they are destroying the spirit of alliance," he said.
The threat came hours after Mr Al Baker complained about protectionism from certain parts of the US and Europe.
The three big US carriers - American, Delta and United - are pushing their government to restrict market access for the Gulf carriers.
They argue that their rivals in the Middle East have received $42bn (Â£27bn) in unfair state aid, a charge that Emirates, Etihad and Qatar Airways deny.
The bitter dispute has been hard to ignore at the annual IATA meeting.  Instead of celebrating a record period of profitability, the row has exposed the deep divisions in the airline industry.
Qatar Airways boss Akbar Al Baker has threatened to leave the Oneworld alliance, accusing American Airlines of blocking his carrier's business.