The eggs were produced by duck farmers in neighbouring Hebei province who are suspected of adding the dye to the animals' feed to give the yolks a more intense red colour.
Chinese consumers pay more for eggs with red yolks as they believe the red colour is a sign of quality and better nutrition.
Some people think that the eggs become red from the shrimp in ducks' diets.
However Hou Shuisheng, a researcher from the Chinese Academy of Agricultural Science, told AP-foodtechnology that for ordinary eggs, "the colour of the yolk should be light yellow.
Both bright yellow and bright red yolks are not natural, so it is certain that some dyes have been added" .
While government food safety officials told local media that the amounts of dye found in the eggs (as much as 0.137mg per kg of eggs) would not be dangerous unless consumed in great quantities, the news could heighten a growing lack of faith in the country's food safety standards.
The contaminated eggs have been found in Wumart supermarkets, with more than 10,000 kg already sold, a local franchiser told China Daily .
Beijing has already identified Sudan Red in other food products in recent years, including a vegetable used in KFC's soup and Heinz chilli sauces.
The dye, which is commonly used in industrial products like flooring and shoe polish, has however contaminated food products around the world, and led to hundreds of product recalls in the UK last year.
The contamination was blamed on a chilli powder imported from India and used as an ingredient in a wide range of food brands.
The Beijing Administration for Industry and Commerce told AP-Foodtechnology.com that it is currently checking duck eggs in markets around the city for traces of the dye, listed as a grade 3 carcinogen by international cancer research organisations.
The eggs were produced by farmers raising ducks on Baiyangdian lake, the largest freshwater lake in Hebei, and the main suppliers of duck eggs to Beijing's markets and supermarkets.