The incident, a breach of Article 29.1 of the FIA sporting regulations, occurred during the latter stages of the second and final Friday practice session at Sakhir.
Magnussen was following Red Bull's Daniil Kvyat to the pit lane, but the stewards did not deem that an acceptable reason to not stop, and opted to sanction the Dane.
"The driver failed to stop for weighing during P2 when signalled to do so by the red traffic light, the car was not returned to the FIA garage and work was undertaken," a statement from the stewards read.
"In accordance with Article 29.1 iv) of the FIA Formula One Sporting Regulations the driver is required to start from the pit lane."
Magnussen was 16th fastest in FP2, and 15th in FP1.