Long COVID (LC) following SARS-CoV-2 infection affects millions of individuals world-wide and manifests with a variety of symptoms including cognitive dysfunction also known as "brain fog". This is characterized by difficulties in executive functions, planning, decision-making, working memory, impairments in complex attention, loss of ability to learn new skills and perform sophisticated brain tasks. No effective treatment options currently exist for LC-related cognitive dysfunction. Here, we use the IntelliCage, which is an automated tracking system of cognitive functions, following SARS-CoV-2 infection in mice, measuring the ability of each mouse within a group to perform tasks that mimic complex human behaviors, such as planning, decision-making, cognitive flexibility, and working memory. Artificial intelligence and machine learning analyses of the tracking data classified LC mice into distinct behavioral categories from non-infected control mice, permitting precise identification and quantification of complex cognitive dysfunction in a controlled, replicable manner. Importantly, we find that brains from LC mice with cognitive dysfunction exhibit transcriptomic alterations similar to those observed in humans suffering from LC-related cognitive impairments, including altered expression of genes involved in learning, executive functions, synaptic functions, neurotransmitters and memory. Together, our findings establish a validated murine model and an automated unbiased approach to study LC-related cognitive dysfunction for the first time, and providing a valuable tool for screening potential treatments and therapeutic interventions.