Polymer solutions in the vicinity of the theta-point are known to undergo shear-induced turbidity or phase separation. The present study shows that a similar phenomenon also occurs for certain wormlike micellar solutions. Wormlike micelles are the self-assembled counterparts of polymers and are characterized by their ability to reversibly break and recombine. In the system of interest, the micelles are formed by the cationic surfactant erucyl bis(hydroxyethyl)methylammonium chloride (EHAC), in conjunction with a salt such as sodium chloride (NaCl) or sodium salicylate (NaSal). Micellar samples that become turbid under shear show evidence of critical concentration fluctuations and may contain predominantly branched micelles. The shear-induced turbidity in these samples correlates with the appearance of flow-dichroism in rheooptic experiments and with an increase in low-q scattering in small-angle light scattering under flow (flow-SALS) experiments. The characteristic "butterfly" pattern, with enhanced scattering in the flow direction and a dark streak perpendicular to the flow direction, is typically observed in flow-SALS. The results suggest that the turbidity is due to a shear-induced growth of concentration fluctuations, which in turn manifests as large anisotropic domains, typically oriented along the vorticity axis.