An apparatus for determining a closure pressure of a fractured formation surrounding a wellbore is disclosed. The apparatus, in one embodiment, includes an isolation device for isolating a section of the wellbore, a fluid supply unit for supplying a fluid from the wellbore under pressure into the isolated section of the wellbore to cause a fracture in the formation proximate the isolated section, a receiving unit for receiving fluid from the isolated section at a constant or substantially constant rate due to pressure difference between the formation and the receiving unit, and a sensor for determining pressure of the formation during receiving of the fluid into the receiving unit. The apparatus further includes a controller for determining the closure pressure from the determined pressure.