This study investigates the effect of graphene scaffold on morphology, viability, cytoskeleton, focal contacts, mitochondrial network morphology and activity in BALB/3T3 fibroblasts and provides new data on biocompatibility of the “graphene-family nanomaterials”. We used graphene monolayer applied onto glass cover slide by electrochemical delamination method and regular glass cover slide, as a reference. The morphology of fibroblasts growing on graphene was unaltered, and the cell viability was 95% compared to control cells on non-coated glass slide. There was no significant difference in the cell size (spreading) between both groups studied. Graphene platform significantly increased BALB/3T3 cell mitochondrial activity (WST-8 test) compared to glass substrate. To demonstrate the variability in focal contacts pattern, the effect of graphene on vinculin was examined, which revealed a significant increase in focal contact size comparing to control-glass slide. There was no disruption in mitochondrial network morphology, which was branched and well connected in relation to the control group. Evaluation of the JC-1 red/green fluorescence intensity ratio revealed similar levels of mitochondrial membrane potential in cells growing on graphene-coated and uncoated slides. These results indicate that graphene monolayer scaffold is cytocompatible with connective tissue cells examined and could be beneficial for tissue engineering therapy.