Context: The knowledge of the binary properties of metal-poor and solar-metallicity stars can shed light on the potential differences between the formation processes responsible for both types of objects. Aims: The aim of the project is to determine the binary properties (separation, mass ratio, frequency of companions) for M subdwarfs, the low-metallicity counterparts of field M dwarfs, and investigate any potential differences between both populations. Methods: We have obtained high-resolution imaging in the optical for a sample of 24 early-M subdwarfs and nine extreme subdwarfs with the “Lucky Imaging” technique using the AstraLux instrument on the Calar Alto 2.2-m telescope. Results: We are sensitive to companions at separations larger than 0.1 arcsec and differences of ~2 mag at 0.1 arcsec and ~5 mag at 1 arcsec. We have found no companion around the 24 subdwarfs under study and one close binary out of nine extreme subdwarfs. A second image of LHS 182 taken three months later with the same instrument confirms the common proper motion of the binary separated by about 0.7 arcsec. Moreover, we do not confirm the common proper motion of the faint source reported by Riaz and collaborators at ~2 arcsec from LHS 1074. Conclusions: We derive a binary frequency of 3±3% for M subdwarfs from our sample of 33 objects for separations larger than about five astronomical units. Adding to our sample the additional 28 metal-poor early-M dwarfs observed with the Hubble Space Telescope by Riaz and collaborators, we infer a binary fraction of 3.7±2.6% (with a 1σ confidence limit), significantly lower than the fraction of resolved binary M dwarfs (~20%) over the same mass and separation ranges. This result suggests a sharp cut-off in the multiplicity fraction from G to M subdwarfs, indicating that the metallicity plays a role at lower masses and/or an environmental effect governing the formation of metal-poor M dwarfs compared to their metallicity counterparts. Based on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC).