Early B-type stars with initial masses between 8 and 15 M⊙ are frequently found in multiple systems, as is evidenced by multi-epoch spectroscopic campaigns in the Milky Way and the Large Magellanic Cloud (LMC). Previous studies have shown no strong metallicity dependence in the close-binary (a < 10 au) fraction or orbital-period distributions between the Milky Way's solar metallicity (Z⊙) and that of the LMC (Z = 0.5 Z⊙). However, similar analyses for a large sample of massive stars in more metal-poor environments are still scarce. We focus on 309 early B-type stars (luminosity classes III-V) from the Binarity at LOw Metallicity (BLOeM) campaign, which targeted nearly 1000 massive stars in the Small Magellanic Cloud (SMC, Z = 0.2 Z⊙) using VLT/FLAMES multi-epoch spectroscopy. By applying binary detection criteria consistent with previous works on Galactic and LMC samples, we identify 153 stars (91 SB1, 59 SB2, 3 SB3) exhibiting significant radial-velocity (RV) variations, resulting in an observed multiplicity fraction of fmultobs = 50 ± 3%. Using Monte Carlo simulations to account for observational biases, we infer an intrinsic close-binary fraction of fmult = 80 ± 8%. This fraction reduces to ∼55% when increasing our RV threshold from 20 to 80 km s‑1; however, an independent Markov chain Monte Carlo analysis of the peak-to-peak RV distribution (ΔRVmax) confirms a high multiplicity fraction of fmult = 79 ± 5%. These findings suggest a possible anti-correlation between metallicity and the fraction of close B-type binaries, with the SMC multiplicity fraction significantly exceeding previous measurements in the LMC and the Galaxy. The enhanced fraction of close binaries at SMC's low metallicity may have broad implications for massive-star evolution in the early Universe. More frequent mass transfer and envelope stripping could boost the production of exotic transients, stripped supernovae, gravitational-wave progenitors, and sustained UV ionising flux, potentially affecting cosmic reionisation. Theoretical predictions of binary evolution under metal-poor conditions will provide a key test of our results.