Headwinds over the past four days exceeded 200 knots, which can burn up to 15 percent more fuel on its Boeing 777-200 aircraft, it said.
It lifted the ban less than 24 hours after imposing it after concluding it could take a shorter route.
The airline in an e-mail said it does a daily risk assessment to determine the most optimum route for flights and that currently, it is taking "a more northerly route." It didn't elaborate.
It said on Tuesday unusually intense headwinds were jeopardising the ability of aircraft to reach cities in the continent even with a full load of fuel.
The airline warned that any luggage that was checked in would "arrive later," while customers connecting with Malaysian flights via other members of the Oneworld alliance may have had their bags offloaded.
Routes were modified after the downing of one of its jets over a war-zone in Ukraine in 2014 killed all 298 people aboard.
"The reasoning has made them look odd, it's pure stupidity," said Shukor Yusof, founder of Endau Analytics, an aviation consultancy firm in Malaysia.
"It's ludicrous. Malaysia Airlines have been flying to Europe for decades. Over the last 30-40 years was there no bad weather?"
Sad to see this Malaysian icon crumble with service excuses like this.
Tuesday's baggage plan was also widely criticised over the internet.
"Sad to see this Malaysian icon crumble with service excuses like this," wrote Patrick Khoo, who identified himself as a traveller from Kuala Lumpur, in a Facebook posting.
The past two years have been tumultuous for the carrier starting with the mysterious disappearance of MH370, which went missing in March 2014 while on a routine flight to Beijing from its base in Kuala Lumpur. Wreckage of the plane hasn't been found in the world's biggest search for a missing plane. The airline's website got hacked, losses mounted and another aircraft was downed in Ukraine. Malaysia's government then had to take the airline private, fire employees and appointed a new chief executive to restructure.
As part of the plan to turn around the carrier, chief executive Christoph Mueller took an unusual step last month by agreeing on a mammoth deal with Dubai-based Emirates.
The plan gave the carrier access to Europe without incurring "monumental losses," Mueller said in an interview at the time.
Malaysia Air said it regretted the inconvenience to passengers "and will deliver stranded baggage as soon as the situation permits". The carrier said in the bulletin that it would "continue to assess the changing situation".
Malaysia Air's no-baggage plan, not shared by any other Asian airline, comes even as global oil prices have declined to around their lowest in a decade. Singapore Airlines increased baggage allowance in all classes starting November 2013. Passengers flying on Singapore Air's suites and first class can check in 50kg of bags, those on business class 40kg and economy class 30kg.
Singapore Air has no plan to change its check-in baggage policy, the carrier said in an emailed statement.
Malaysia Air has been under intense scrutiny since MH370 went missing almost two years ago. Last month, the airline began investigating why Auckland's air traffic control was provided with a wrong flight plan after the pilot questioned the air route.
The carrier's "Bucket List" advertisement campaign in September 2014 sparked criticism across social media. The airline later said it will stop the "inappropriate" campaign in New Zealand and Australia.
- AP, Bloomberg.
