An inking unit in a printing machine, formed as a film inking unit, includes an ink duct with an ink duct film inserted between an ink metering system, which is subdivided into ink zones, and an ink duct roller. The ink duct film within each of the ink zones in a region of a settable metering gap is held out of contact with the ink duct roller during printing. The invention also includes a printing machine, such as a sheet-fed printing machine, particularly, provided with the inking unit.