After the detection of a 321-days periodicity in X-rays, HESS J0632+057 can be robustly considered a new member of the selected group of gamma-ray binaries. These sources are known to show extended radio structure at scales of milliarcseconds (mas). Aims. We present the expected extended radio emission on mas scales from HESS J0632+057. Methods. We observed HESS J0632+057 with the European VLBI Network (EVN) at 1.6 GHz in two epochs: during the January/February 2011 X-ray outburst and 30 days later. Results. The VLBI image obtained during the outburst shows a compact ~0.4 mJy radio source, whereas 30 days later the source has faded and appears extended, with a projected size of ~75 AU. The peak of the emission is displaced between runs 21+/-5 AU, which is bigger than the orbit size. The position of the radio source is compatible with the Be star MWC 148, which sets the proper motion of the binary system below 3 mas yr^-1 in each coordinate. The brightness temperature of the source is above 2 \times 10^6 K. We compare the multiwavelength properties of HESS J0632+057 with those of the previously known gamma-ray binaries. Conclusions. HESS J0632+057 displays extended and variable non-thermal radio emission. Its morphology, size, and displacement at AU scales are similar to those found in the other gamma-ray binaries, PSR B1259-63, LS 5039 and LS I +61 303, supporting a similar nature for HESS J0632+057.