How stress affects functional hemispheric asymmetries is relevant because stress represents a risk factor for the development of mental disorders and various mental disorders are associated with atypical lateralization. Using three lateralization tasks, we investigated whether functional hemispheric asymmetries in the form of hemispheric dominance for language (verbal dichotic listening task), emotion processing (emotional dichotic listening task), and visuo-spatial attention (line bisection task) were affected by acute stress in healthy adults. One hundred twenty right-handed men and women performed these lateralization tasks in randomized order after exposure to a mild online stressor (i.e., an online variant of the Trier Social Stress Test (TSST), TSST-OL) and a non-stressful online control task (friendly TSST-OL, fTSST-OL) in a within-subjects design. Importantly, the verbal and the emotional dichotic listening tasks were presented online whereas the line bisection task was completed in paper–pencil form. During these tasks, we found the expected hemispheric asymmetries, indicating that online versions of both the verbal and the emotional dichotic listening task can be used to measure functional hemispheric asymmetries in language and emotion processing remotely. Even though subjective and physiological markers confirmed the success of the online stress manipulation, replicating previous studies, we found no stress-induced effect on functional hemispheric asymmetries. Thus, in healthy participants, functional hemispheric asymmetries do not seem to change flexibly in response to acute stress.