We report on observations of the Be/X-ray binary system Swift J1626.6-5156 performed with the Nuclear Spectroscopic Telescope ARray (NuSTAR) during a short outburst in 2021 March, following its detection by the MAXI monitor and Spektrum-Roentgen-Gamma (SRG) observatory. Our analysis of the broadband X-ray spectrum of the source confirms the presence of two absorption-like features at energies E ∼ 9 and E ∼ 17 keV. These had been previously reported in the literature and interpreted as the fundamental cyclotron resonance scattering feature (CRSF) and its first harmonic (based on Rossi X-ray Timing Explorer (RXTE) data). The better sensitivity and energy resolution of NuSTAR, combined with the low-energy coverage of Neutron star Interior Composition Explorer (NICER), allowed us to detect two additional absorption-like features at E ∼ 4.9 keV and E ∼ 13 keV. Therefore, we conclude that, in total, four cyclotron lines are observed in the spectrum of Swift J1626.6-5156: the fundamental CRSF at E ∼ 4.9 keV and three higher spaced harmonics. This discovery makes Swift J1626.6-5156 the second accreting pulsar, after 4U 0115+63, whose spectrum is characterized by more than three lines of a cyclotronic origin, and implies that the source has the weakest confirmed magnetic field among all X-ray pulsars, B ∼ 4 x 10¹¹ G. This discovery makes Swift J1626.6-5156 one of the prime targets for the upcoming X-ray polarimetry missions covering the soft X-ray band, such as Imaging X-ray Polarimetry Explorer (IXPE) and enhanced X-ray Timing and Polarimetry mission (eXTP).