Wiper device for blown glass or plastic container, including a hollow body having a first and a second end defining respectively a first and a second opening, a flange extending from an outer surface of the hollow body at the first end, and a wiper element extending from an inner surface of the hollow body, the wiper element defining a passage with a smaller section than the first and second openings, the hollow body featuring at least one first row and one second row of flexible fins extending from the outer surface of the hollow body, near the second end The second row of flexible fins, which is closer to the second end in respect to the first row has, in a non-flexed configuration, a diameter greater than the diameter of the first row of fins in a non-flexed configuration.