We present results of the multiwavelength campaign on the TeV blazar Mkn 501 performed in 2006 July, including MAGIC for the very-high-energy (VHE) γ-ray band and Suzaku for the X-ray band. A VHE γ-ray signal was clearly detected with an average flux above 200 GeV of ~20% of the Crab Nebula flux, which indicates a low state of source activity in this energy range. No significant variability has been found during the campaign. The VHE γ-ray spectrum can be described by a simple power law from 80 GeV to 2 TeV with a photon index of 2.8 ± 0.1, which corresponds to one of the steepest photon indices observed in this energy range so far for this object. The X-ray spectrum covers a wide range from 0.6 to 40 keV, and is well described by a broken power law, with photon indices of 2.257 ± 0.004 and 2.420 ± 0.012 below and above the break energy of 3.24+0.13 -0.12 keV. No apparent high-energy cut-off is seen above the break energy. Although an increase of the flux of about 50% is observed in the X-ray band within the observation, the data indicate a consistently low state of activity for this source. Time-resolved spectra show an evidence for spectral hardening with a flux level. A homogeneous one-zone synchrotron self-Compton (SSC) model can adequately describe the spectral energy distribution (SED) from the X-ray to the VHE γ-ray bands with a magnetic field intensity B = 0.313 G and a Doppler beaming factor δ = 20, which are similar to the values in the past multiwavelength campaigns in high states. Based on our SSC parameters derived for the low state, we are able to reproduce the SED of the high state by just changing the Lorentz factor of the electrons corresponding to the break energy in the primary electron spectrum. This suggests that the variation of the injected electron population in the jet is responsible for the observed low-high state variation of the SED.