Nanomechanical cantilever sensors have been emerging as a key device for real-time and label-free detection of various analytes ranging from gaseous to biological molecules. The major sensing principle is based on the analyte-induced surface stress, which makes a cantilever bend. In this letter, we present a membrane-type surface stress sensor (MSS), which is based on the piezoresistive read-out integrated in the sensor chip. The MSS is not a simple "cantilever," rather it consists of an "adsorbate membrane" suspended by four piezoresistive "sensing beams," composing a full Wheatstone bridge. The whole analyte-induced isotropic surface stress on the membrane is efficiently transduced to the piezoresistive beams as an amplified uniaxial stress. Evaluation of a prototype MSS used in the present experiments demonstrates a high sensitivity which is comparable with that of optical methods and a factor of more than 20 higher than that obtained with a standard piezoresistive cantilever. The finite element analyses indicate that changing dimensions of the membrane and beams can substantially increase the sensitivity further. Given the various conveniences and advantages of the integrated piezoresistive read-out, this platform is expected to open a new era of surface stress-based sensing.