Critical infrastructure (such as transportation, water, electric power, wastewater, and telecommunications) provides the conveyance of goods, services, and resources to communities, which are vital for economic activities. Buildings, bridges, and other structures and components of the infrastructure might be subject to natural and anthropogenic hazards, which may lead to a reduction or loss of functionality of infrastructure. Businesses may experience disruptions because of (i) direct damage to the business properties and facilities, (ii) reduction or loss of functionality of the supporting critical infrastructure, or (iii) impact on social systems affecting the availability of the workforce at a specific business and supporting businesses as well as customers. Current approaches do not model the functionality of business properties and supporting infrastructure, generally obtaining only empirical estimates of business interruption losses. Such predictions might not be applicable to different businesses, supporting infrastructure, social systems, locations, and hazards; and they would in general not reflect possible changes in the built environment due to mitigation strategies and interventions. This paper proposes a mathematical formulation that overcomes the limitations in the current approaches. The proposed formulation models and quantifies the likelihood of business interruption with a ground-up approach by incorporating the dependency of business operations on physical structures, infrastructure and social systems. The paper illustrates the proposed formulation by investigating the business interruption of an example food retail store in Seaside, Oregon subject to a seismic hazard.