Context. This work is part of the BinaMIcS project, the aim of which is to understand the interaction between binarity and magnetism in close binary systems. All the studied spectroscopic binaries targeted by the BinaMIcS project encompass hot massive and intermediate-mass stars on the main sequence, as well as cool stars over a wide range of evolutionary stages. Aims. The present paper focuses on the binary system FK Aqr, which is composed of two early M dwarfs. Both stars are already known to be magnetically active based on their light curves and detected flare activity. In addition, the two components have large convective envelopes with masses just above the fully convective limit, making the system an ideal target for studying effect of binarity on stellar dynamos. Methods. We use spectropolarimetric observations obtained with ESPaDOnS at CFHT in September 2014. Mean Stokes I and V line profiles are extracted using the least-squares deconvolution (LSD) method. The radial velocities of the two components are measured from the LSD Stokes I profiles and are combined with interferometric measurements in order to constrain the orbital parameters of the system. The longitudinal magnetic fields B l and chromospheric activity indicators are measured from the LSD mean line profiles. The rotational modulation of the Stokes V profiles is used to reconstruct the surface magnetic field structures of both stars via the Zeeman Doppler imaging (ZDI) inversion technique. Results. Maps of the surface magnetic field structures of both components of FK Aqr are presented for the first time. Our study shows that both components host similar large-scale magnetic fields of moderate intensity (B mean ≃ 0.25 kG); both are predominantly poloidal and feature a strong axisymmetric dipolar component. Conclusions. Both components of FK Aqr feature a rather strong large-scale magnetic field (compared to single early M dwarfs with similar masses) with a mainly dipolar axisymmetric structure. This type of magnetic field is not typical for single early M dwarfs, and is rather reminiscent of fully convective dwarfs with later spectral types. The primary FK Aqr A is currently the most massive recognised main sequence M dwarf known to host this type of strong dipolar field.