Vietnam does not have a formal regulation barring pets from entering the country. However it's a long trip to Vietnam and one should bear in mind that this journey is not always easy for a pet to endure as in most cases the pet will be in the luggage compartment of a commercial airliner for many hours and may or may not be allowed access to the country when finally arriving at the destination.
Vietnam, like most places in Asia can be very hard on pets. It is not advisable to bring pets and allow them to run and play outdoors unless they are closely watched and brought back inside when finished. Items like cat litter are not readily available in Vietnam. Varieties of pet foods are also rather limited in Vietnam. In short, if you absolutely must bring a pet with you to Vietnam, please take every possible action to ensure your pet's safety and comfort.