Context. Magnetic fields are good tracers of gas compression by shock waves in the interstellar medium. These can be caused by the interaction of star-formation driven outflows from individual star formation sites as described in the chimney model. Integration along the line-of-sight and cosmic-ray diffusion may hamper detection of compressed magnetic fields in many cases. Aims. We study the magnetic field structure in the central part of the nuclear starburst galaxy NGC 253 with spatial resolutions between 40 and 150 pc to detect any filamentary emission associated with the nuclear outflow. As the nuclear region is much brighter than the rest of the disc we can distinguish this emission from that of the disc. Methods. We used radio polarimetric observations with the VLA. New observations at λ3 cm with 7. 5 resolution were combined with archive data at λλ 20 and 6 cm. We created a map of the rotation measure distribution between λλ 6 and 3 cm and compared it with a synthetic polarization map. Results. We find filamentary radio continuum emission in a geometrical distribution, which we interpret as the boundary of the NW nuclear outflow cone seen in projection. The scaleheight of the continuum emission is 150 ± 20 pc, regardless of the observing frequency. The equipartition magnetic field strength is 46 ± 10 μG for the total field and 21 ± 5 μG for the regular field in the filaments. We find that the ordered magnetic field is aligned along the filaments, in agreement with amplification due to compression. The perpendicular diffusion coefficient across the filaments is κ ⊥ = 1.5 × 10 28 cm 2 s −1 · E(GeV) 0.5±0.7 . In the SE part of the nuclear outflow cone the magnetic field is pointing away from the disc in form of a helix, with an azimuthal component increasing up to at least 1200 pc height, where it is about equal to the total component. The ordered magnetic field in the disc is anisotropic within a radius of 2.2 kpc. At larger radii, the large-scale field is regular and of even parity. Conclusions. The magnetic filaments indicate an interaction of the nuclear outflow with the interstellar medium. The magnetic field is able to collimate the outflow, which can explain the observed small opening angle of ≈26 • . Owing to the conservation of angular momentum by the plasma in the nuclear outflow, the field lines are frozen into the plasma, and they wind up into a helix. Strong adiabatic losses of the cosmic-ray electrons in the accelerated outflow can partly explain why the radio luminosity of the nucleus lies below the radio-FIR correlation.