Magnetic spin fluctuations is one candidate to produce the bosonic modes that mediate the superconductivity in the ferrous superconductors. Up until now, all of the LaOFeAs and BaFe2As2 structure types have simple commensurate magnetic ground states, as result of nesting Fermi surfaces. This type of spin-density-wave (SDW) magnetic order is known to be vulnerable to shifts in the Fermi surface when electronic densities are altered at the superconducting compositions. Superconductivity has more recently been discovered in alpha-Fe(Te,Se), whose electronically active antifluorite planes are isostructural to the FeAs layers found in the previous ferrous superconductors and share with them the same quasi-two-dimensional electronic structure. Here we report neutron scattering studies that reveal a unique complex incommensurate antiferromagnetic order in the parent compound alpha-FeTe. When the long-range magnetic order is suppressed by the isovalent substitution of Te with Se, short-range correlations survive in the superconducting phase.