Navigational risk for ships has always been a key focus in maritime traffic safety research, with a variety of risk assessment methods available, each possessing its own advantages. In the era of big data, with the diversification of information and the deep application of system safety, this study addresses the navigational risks of ships in Arctic ice regions from a complex systems perspective. Taking the Arctic Northeast Passage as an example, a quantitative assessment model for navigational risk in Arctic waters is constructed using stochastic Petri nets (SPN). This model analyzes the mechanism of the navigational process and provides risk control schemes specifically targeting high-risk factors. The research findings indicate that sea ice density is a pivotal factor in the navigational risk of ships traversing the Arctic Northeast Passage. The risk for ships navigating the East Siberian Sea, Laptev Sea, and Kara Sea (especially the Vilkitsky Strait) is heightened due to persistent sea ice even during the summer season. Icebreaker assistance is deemed necessary when sailing in spring and autumn.