Abnormalities of the Language Network (LN) have been found in different psychiatric conditions (e.g., schizophrenia and bipolar disorder), supporting the hypothesis that language plays a central role in a high-level integration/connectivity of second-level cognitive processes and the underlying cortical regions. This view implies a continuum of shared neural alterations along the psychotic disorder spectrum. In particular, bipolar disorder (BD) patients were recently documented to have an altered LN asymmetry during resting state. The extent to which the LN architecture is altered and stable also during a language task has yet to be investigated. To address this question, we analyzed fMRI data recorded during an open-eyes resting state session and a silent verbal fluency task in 16 euthymic BD patients and 16 matched healthy controls (HC). Functional connectivity in the LN of both groups was computed using spatial independent component analysis, and group comparisons were carried out to assess the network organization during both rest and active linguistic task conditions. The LN of BD patients involved left and right brain areas during both resting state and linguistic task. Compared to the left-lateralized network found in HC, the BD group was characterized by two anterior clusters (in left frontal and right temporo-insular regions) and the disengagement of the posterior language areas, especially during the verbal fluency task. Our findings support the hypothesis that reduced language lateralization may represent a biological marker across different psychotic disorders and that the altered language network connectivity found at rest in bipolar patients is stable and pervasive as it is also impaired during a verbal fluency task.