The invention relates to a tool holder (10) for a cutting insert (18), having a shank (12), a counter bearing (14) on which a pocket (16) for a cutting insert (18) is provided, disposed on the front end of the shank, and a clamping segment (20) integrally joined to the shank (12) via a bending segment (22); wherein the clamping segment (20) has a clamping finger (28) and a clamping element (26) such that the clamping finger (28) is capable of acting against the counter bearing segment (14) by means of the clamping element (26), thereby enabling a cutting insert (18) to be clamped between the clamping finger (28) and the counter bearing segment (14); wherein the clamping segment (20) protrudes beyond the top side of the shank (12); and wherein a coolant supply passage (40, 42, 44, 46) extends through the shank (12) and the bending segment (22) into the clamping segment (20); wherein the coolant supply passage (40, 42, 44, 46) has a shank passage (46), a clamping finger passage (40), and a connecting passage (44) that starts from the shank passage (46) and extends through the bending segment (22); characterized in that the connecting passage (44) is disposed in a longitudinal center region of the tool holder (10) and, on its rear side (30) facing toward the shank (12), the clamping segment (20) extends less far in a direction toward the rear end of the shank (12) on both sides of the longitudinal center segment than it does in the longitudinal center segment.