A MEMS flow sensor has a flow channel that avoids wire bond pads and ancillary circuit elements. A fluid can move from the bottom of the sensor substrate, though an inlet hole, over a sensing element on the top of the substrate, and then through an outlet hole. The inlet hole and the outlet hole can pass from the substrate top to the substrate bottom. A top cap can be fixed to the top of the substrate such that it covers the sensing element, the inlet hole, and the outlet hole. The top cap constrains the flow channel and keeps fluid, either gaseous or liquid, from exiting the channel and contacting the wire bond pads or ancillary circuit elements.