The inquiry will be headed by retired High Court judge Ian Callinan, who will have sweeping powers to investigate "every aspect" of the crisis, Howard told reporters here.
"We are determined to find out what happened, how this disease was introduced, whether there's been a breach of quarantine procedures and protocols," Howard said.
Callinan will "be able to require people to give evidence, produce documents and he will conduct public hearings if he regards that as being necessary," the prime minister said.
Racing in the states of New South Wales and Queensland has been suspended indefinitely as a result of the outbreak, which was first detected 10 days ago at a quarantine centre in the western outskirts of Sydney.
An internal investigation is now under way at the facility, where stallions had arrived from overseas in early August.
Equine influenza is a highly contagious virus that is harmless to humans but causes respiratory problems, fever and sometimes death in horses.
"The inquiry is what we asked for," said Peter V'Landys, chief executive of Racing NSW, adding that it was vital to find out how the disease got into Australia.
Agriculture Minister Peter McGauran has said quarantine failure was a logical conclusion to make, adding the virus "almost certainly" originated in Japan.
The virus has since spread to stables at Sydney's Royal Randwick racecourse, forcing the cancellation of spring races and crippling the multi-billion-dollar industry for almost a week as authorities tried to contain the outbreak.
The government is also considering a wage subsidy scheme for affected industry workers. Howard said Sunday that further announcements would be made on compensation in the coming days.