In the lawsuit, Aldi is accused of trademark infringement, unfair competition and unjust enrichment. Mondelēz said it is seeking damages.
Mondelēz described Aldi's business model as hinging on "low-priced private label products that resemble the look and feel of well-known brands".
Aldi, which has its headquarters in Germany, is known as a discount supermarket offering affordable alternatives to well-known brands.
There are over 2,500 Aldi shops in the US.
This is not the first time Aldi has been embroiled in a trademark battle. Earlier this year, it lost a battle with Cider producers Thatchers, which accused the supermarket of copying its drink in "taste and appearance".