The handset went on sale for a price of 16,999 yuan (£1,900) via Huawei's online store and reportedly sold out out "within minutes".
Phone fans who did not manage to buy a Mate X on Friday will get another chance on 22 November when a second batch will go on sale.
Anyone buying one of the folding devices also gets 50% off screen-related repairs and replacements.
Accidental damage?
The 5G Mate X is available in one model featuring an 8in (20.3cm) screen when unfolded. When closed it has two screens - one 6.8in and the smaller one 6.6in.
Huawei said the phone was available in "limited quantities" for the first sale but did not give a precise number on how many were sold.
Growing numbers of phone-makers are starting to offer foldable devices. Samsung, Xiaomi and Motorola have both made flexible devices alongside smaller players such as Royole. Other phone-makers, including Apple and Google, are known to be experimenting with their own designs.
The Huawei device was initially due to go on sale in June but the launch was delayed following the imposition of sanctions by the US.
The phone is currently available only in China but Huawei has said it will be available in other countries at some point.
Ben Wood, from analyst CCS Insight, said he was "increasingly sceptical" about Huawei's folding phone after using the Samsung Galaxy Fold for a few weeks and spending some time with the just-released Motorola Razr.
Huawei's decision to put the screen on the outside of the phone made it "incredibly vulnerable" to accidental damage, he said.
"That risk, the eye-watering price and the decision to only ship it in China makes me wonder whether it is a super niche device that was more about Huawei demonstrating 'the art of the possible' rather than having a credible commercial product," he told the BBC.
