A method for estimating fracture aperture from multi-axial electromagnetic induction measurements made in a wellbore includes determining a fracture indicator and a fracture orientation indicator. The value of the fracture indicator is determined from components of the measurements made transverse to the tool axis. A relationship between the value of the fracture indicator and the fracture aperture for the subsurface formation is determined by estimating the fracture indicator using a plurality of values of fracture aperture and a resistivity of drilling fluid in the wellbore over a background formation with estimated horizontal resistivity and vertical resistivity. The fracture aperture is determined using the determined fracture indicator and the determined relationship.