An apparatus and method for gripping a syringe utilizes four gripping members advanceable in different corresponding directions toward a predetermined axis to supportably engage a barrel of a syringe at corresponding circumferentially offset locations. A first motor may be utilized for co-driven advancement of the gripping members in tandem in the different corresponding directions toward the predetermined axis, and for retraction of the gripping members. The gripping members may include corresponding rollers, wherein a single one of the rollers may be rotated in an automated manner during supportive engagement of a syringe by the gripping members. A second motor may be utilized for driven rotation of the single roller. The disclosed embodiments may be utilized for supportive engagement of syringes having a range of syringe diameters.