Context. The existence of accreting supermassive black holes of up to billions of solar masses at early cosmological epochs (in the context of this work, redshifts z ≳ 6) requires very fast growth rates that are challenging to explain. The presence of a relativistic jet can be a direct indication of activity and accretion status in active galactic nuclei (AGN), constraining the radiative properties of these extreme objects. However, known jetted AGN beyond z ∼ 6 are still very rare. Aims. The radio-emitting AGN J2331+1129 has recently been claimed as a candidate BL Lac object at redshift z = 6.57 based on its synchrotron-dominated emission spectrum and a lack of ultraviolet or optical emission lines. It is a promising candidate for the highest-redshift blazar known to date. The aim of the observations described here is to support or refute the blazar classification of this peculiar source. Methods. We performed high-resolution radio interferometric imaging observations of J2331+1129 using the Very Long Baseline Array at 1.6 and 4.9 GHz in February 2022. Results. The images reveal a compact but slightly resolved, flat-spectrum core feature at both frequencies, indicating that the total radio emission is produced by a compact jet and originates from within a central region of ∼10 pc in diameter. While these details are consistent with the radio properties of a BL Lac object, the inferred brightness temperatures are at least an order of magnitude lower than expected for a Doppler-boosted radio jet, which casts doubt on the high-redshift BL Lac identification.