Chief among food inspectors' concerns is that the illicit horsemeat could contain the veterinary drug phenylbutazone, or "bute," commonly used to treat horses.
Meat from animals treated with phenylbutazone is not allowed to enter the food chain as it may pose a risk to human health.
Findus has been ordered to test the lasagna withdrawn from shelves in the United Kingdom for the drug's presence.
Aldi said in a statement that tests on random samples of its affected products, labeled Today's Special Frozen Beef Lasagne and Today's Special Frozen Spaghetti Bolognese, "demonstrated that the withdrawn products contained between 30% and 100% horse meat.
"This is completely unacceptable and like other affected companies, we feel angry and let down by our supplier. If the label says beef, our customers expect it to be beef."
Samples of the affected Findus lasagna also contained between 60 and 100% horsemeat, according to UK and Irish food safety inspectors.
In January, the Food Safety Authority of Ireland found that 10 out of 27 hamburger products it analyzed in a study contained horse DNA, while 23 of them -- or 85% -- tested positive for pig DNA.
In nine out of the 10 burger samples, the horse DNA was found at very low levels, the inspectors said, but in one sample from Tesco, Britain's largest retailer, the horse meat accounted for about 29% of the burger.
Tesco apologized to customers after the revelation and promised action to make sure it never happened again.
The discovery of pig DNA in beef products is of particular concern to Jews and Muslims, whose dietary laws proscribe the consumption of pig products. Jewish dietary laws also ban the eating of horsemeat.
The Justice Ministry confirmed last week that a number of meat pies and similar items supplied to prisons in England and Wales were labeled and served as halal -- prepared in compliance with Islamic dietary law -- but contained traces of pork DNA, the Food Standards Agency said.
Horsemeat is not commonly eaten in the United States, but the country does export it to Canada and Mexico. Congress passed a bill in November 2011 that lifted a 5-year-old ban on the slaughter of horses for meat in the United States.