The photo was posted online Thursday with Beckham's caption: "I'm all for fans taking a picture but not sure this is the safest way to do it!"
So far it has attracted over 18,000 comments.
Many commentators said they were embarrassed about the image it showed of the country. Facebook user Van Dang Yeu wrote: "This is an ugly face of Vietnam."
Commentator Minh Anh wrote: "A baby in her lap? That's crazy."
The photo attracted widespread coverage in local newspapers and television over the weekend, with many articles pointing out that the woman was breaking the law.
An article in Phap Luat newspaper quoted the chief of Hanoi's Traffic Police as saying the woman could face a fine of 300,000 dong (around 15 dollars) for not wearing a helmet and for using a mobile phone while driving.
Beckham was in Vietnam as part of a tour to promote a new brand of whisky. He travelled to China, Malaysia, Singapore and South Korea, according to his official Facebook page.
With poor law enforcement and congested roads, traffic safety is a lingering problem in Vietnam. About 14,000 people lose their lives each year in the country as a result of road crashes, according to the World Health Organisation.