To date, only humans have been affected by the new A/H1N1 virus, and it is unknown whether the virus will impact other animals, the ASPCA says.
Although the virus is being termed "swine flu", researchers have not confirmed that this new strain evolved in pigs and are working to determine more about its origins.
"At this time there is no data demonstrating any risk of dogs and cats contracting this strain of the virus," says Dr Louise Murray, the director of medicine at the ASPCA's Bergh Memorial Hospital in New York City.
"However, owners of pet pigs, as well as farmers, should monitor their animal's health more closely during this outbreak. Steps to limit possible transmission from humans to pigs and vice versa are recommended."
The ASPCA recommends keeping pet pigs and swine farms isolated from any public exposure that might put them at risk for illness.
The American Association of Swine Veterinarians has suggested that visitors should not be allowed into swine production units, and for humans to avoid unnecessary contact with pigs.
Dr Miranda Spindel, director of the ASPCA's Veterinary Outreach programme, says swine influenza or swine flu is caused by infection with Influenza A viruses and is one of the leading causes of respiratory disease in pigs throughout the world.
Like most Influenza A viruses, swine flu generally causes large numbers of illness in pigs, but fatalities are uncommon.
"Although people do not normally contract swine influenza, humans have become infected when in contact with infected pigs or contaminated environments. Normally, human-to-human transmission of swine flu is temporary. However, as outbreaks have occurred in the past, swine flu is recognised for its potential to cause public health concern."
The ability of any virus to cross species barriers and sustain transmission is dependent on many factors and occurs infrequently.
Like all influenza viruses, swine flu viruses change constantly.
Pigs are unique in that they are able to host both avian and mammalian influenza viruses. It has been suggested that pigs act as a reservoir, allowing avian influenza to adapt to mammalian species, thereby undergoing genetic changes and emerging as entirely new and different viruses.
When these mutated viruses appear, there is potential for humans to become infected and transmit the new virus among other people. The form of influenza that appears to have originated recently in Mexico is a never-before-seen genetic mixture of type A Influenza viruses originating in pigs, birds and people.