Context. Solar Orbiter is expected to have flown close to the tail of comet C/2019 Y4 (ATLAS) during the spacecraft's first perihelion in June 2020. Models predict a possible crossing of the comet tails by the spacecraft at a distance from the Sun of approximately 0.5 AU. Aims. This study is aimed at identifying possible signatures of the interaction of the solar wind plasma with material released by comet ATLAS, including the detection of draped magnetic field as well as the presence of cometary pick-up ions and of ion-scale waves excited by associated instabilities. This encounter provides us with the first opportunity of addressing such dynamics in the inner Heliosphere and improving our understanding of the plasma interaction between comets and the solar wind. Methods. We analysed data from all in situ instruments on board Solar Orbiter and compared their independent measurements in order to identify and characterize the nature of structures and waves observed in the plasma when the encounter was predicted. Results. We identified a magnetic field structure observed at the start of 4 June, associated with a full magnetic reversal, a local deceleration of the flow and large plasma density, and enhanced dust and energetic ions events. The cross-comparison of all these observations support a possible cometary origin for this structure and suggests the presence of magnetic field draping around some low-field and high-density object. Inside and around this large scale structure, several ion-scale wave-forms are detected that are consistent with small-scale waves and structures generated by cometary pick-up ion instabilities. Conclusions. Solar Orbiter measurements are consistent with the crossing through a magnetic and plasma structure of cometary origin embedded in the ambient solar wind. We suggest that this corresponds to the magnetotail of one of the fragments of comet ATLAS or to a portion of the tail that was previously disconnected and advected past the spacecraft by the solar wind.