It is "extremely unlikely" that anyone who has consumed affected horse meat will suffer harmful side effects, she said in a statement Thursday.
"Phenylbutazone... is a commonly used medicine in horses. It is also prescribed to some patients who are suffering from a severe form of arthritis," Davies added.
"At the levels of bute that have been found, a person would have to eat 500 to 600 burgers a day that are 100% horse meat to get close to consuming a human's daily dose. And it passes through the system fairly quickly, so it is unlikely to build up in our bodies," she explained.
German supermarket chain Real confirmed Wednesday that samples of a frozen beef lasagna had tested positive for horse meat. Fellow supermarket chains Rewe and Tengelmann said they are examining certain beef products as a precaution.
Ministers met for emergency talks in Brussels, Belgium, on Wednesday on how to tackle a crisis that has thrown the European meat industry into disarray.
It was already reeling from a bombshell last month, when Irish investigators found horse and pig DNA in a number of hamburger products. The discovery of pig DNA in beef products is of particular concern to Jews and Muslims, whose dietary laws forbid the consumption of pork products. Jewish dietary laws also ban the eating of horse meat.
After Wednesday's talks, Irish Agriculture Minister Simon Coveney said the ministers had agreed to implement measures including random DNA testing of processed beef products across the European Union's 27 member states.
The United Kingdom is awaiting the outcome of "authenticity" tests on beef products ordered last week by the Food Standards Agency across the UK food industry. The results are due by Friday.
Investigations into what could be criminal fraud somewhere in the supply chain also are being led by Europol, the European Union's law enforcement agency.
UK Environment Secretary Owen Paterson, who met with Europol officials Thursday, said, "This is an incredibly important step. It's increasingly clear that this case reaches right across Europe.
"It's clear that Europol is the right organization to coordinate efforts to uncover all wrongdoing and bring criminals to justice, wherever there may be."
Meanwhile, steps have been taken to tighten up the legitimate slaughter of horses in the United Kingdom.
Beginning January 30, the Food Standards Agency ordered 100% testing of horse carcasses, and, as of this week, their meat will not be allowed to enter the food chain until the all-clear has been given.
Previously, a random sample was tested. In 2012, 6% of horse carcasses tested positive for bute, the agency said.