Results of developing and testing graphene-based sensors capable of detecting protein molecules are presented. The biosensor operation was checked using an immunochemical system comprising fluorescein dye and monoclonal antifluorescein antibodies. The sensor detects fluorescein concentration on a level of 1–10 ng/mL and bovine serum albumin–fluorescein conjugate on a level of 1–5 ng/mL. The proposed device has good prospects for use for early diagnostics of various diseases.