Date: 201708
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: B737 Next Generation Undifferentiated
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Climb
Airspace: Class B ZZZ
ATC / advisory: Tower ZZZ
Aircraft component: Flap/Slat Indication
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Second reporter function: Pilot Flying; First Officer
Anomaly: Aircraft Equipment Problem Critical
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Became Reoriented
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: Takeoff planned for and made from runway XX in ZZZ. FO was the PF. Takeoff was made with a normal rotation rate at Vr; and normal initial climb pitch altitude by the PF. At 'landing gear up' call; PM verified and stated 'Positive rate; landing gear-up' and retracted the landing gear. Almost immediately following landing gear retraction the Stall Warning System stick-shaker activated; the 'why' of which took a moment to process. PM looked at the instruments and saw the Stall warning 'fence' near the aircraft symbol; airspeed in the red band; and the pitch attitude still below Flight Director Commands.PM pushed the throttles up and called out the stick shaker and 'airspeed'. PF kept positive control of the aircraft at all times and shallowed the climb slightly and let the aircraft accelerate straight ahead. PM noted the flaps were still set at 5 throughout the brief encounter. Aircraft was then cleaned up on profile and the climb out remained normal after that. Throughout the climb the PM and PF questioned what had happened and more importantly why; without any logical explanation.During the leg prior the Crew; we applied MEL 27-4-XX for LE Flaps Transit amber light on at Flaps 5 during the previous approach into ZZZ; requiring the QRH to be run and; after landing; application of the MEL before this particular takeoff. At cruise the Captain notified Maintenance Control and Dispatch of the issue. As a further precaution; the performance weight and balance landing data was compared to Dispatch; provided landing data by the Pilots; to reconfirm its validity. The remainder of the flight was uneventful. After landing the Captain refused the aircraft for subsequent flight due to safety concerns and lack of confidence in FMC and Stall Warning System interaction.No [recommendations]. Training provided worked as advertised when it was needed to handle this abnormal situation.

Callback: Reporter stated that the leading edge devices sent a false signal to the stick shaker/stall warning computer which triggered the alert.

Second narrative: [Report narrative contained no additional information.]

Second callback: Reporter stated Maintenance found that the air data computer was sent information that the leading edge devices were in transit caused by a faulty #3 leading edge sensor. This caused an anomaly in the stall warning/stick shaker computer that caused the alert.

Synopsis: B737 flight crew reported a stick shaker event after takeoff and gear retraction caused by a faulty leading edge sensor.