Structural evolution of cyclic and branched-cyclic methanol clusters containing three to six molecules, under the influence of externally applied uniform static electric field is studied within the density functional theory. Akin to the situation for water clusters, the electric field is seen to stretch the intermolecular hydrogen bonds, and eventually break the H-bonded network at certain characteristic threshold field values of field strength in the range 0.009-0.016 a.u., yielding linear or branched structures with a lower energy. These structural transitions are characterized by an abrupt increase in the electric dipole moment riding over its otherwise steady nonlinear increase with the applied field. The field tends to rupture the H-bonded structure; consequently, the number of hydrogen bonds decreases with increasing field strength. Vibrational spectra analyzed for fields applied perpendicular to the cyclic ring structures bring out the shifts in the OH ring vibrations (blueshift) and the CO stretch vibrations (redshift). For a given field strength, the blueshifts increase with the number of molecules in the ring and are found to be generally larger than those in the corresponding water cluster counterparts.