Optical palpation maps stress at the surface of biological tissue into 2D images. It relies on measuring surface deformation of a compliant layer, which to date has been performed with optical coherence tomography (OCT). OCT-based optical palpation holds promise for improved clinical diagnostics; however, the complexity and cost hinder broad adoption. In this Letter, we introduce coherence function-encoded optical palpation (CFE-OP) using a novel optical profilometry technique that exploits the envelope of the coherence function rather than its peak position, which is typically used to retrieve depth information. CFE-OP utilizes a Fabry-Perot laser diode (bandwidth, 2.2 nm) and a single photodiode in a Michelson interferometer to detect the position along the coherence envelope as a function of path length. This technique greatly reduces complexity and cost in comparison to the OCT-based approach. We perform CFE-OP on phantom and excised human breast tissue, demonstrating comparable mechanical contrast to OCT-based optical palpation and the capability to distinguish stiff tumor from soft benign tissue.