We report on the effect of a weak external magnetic field on iodine hyperfine transitions around 514 nm, used for infrared laser frequency stabilization. We use a frequency tripled laser diode operating at 1542.1 nm, to interrogate the iodine vapor inserted into a short sealed quartz cell, surrounded by an efficient solenoid. Thus we create a controlled external magnetic fields whose orientation is longitudinal to the counter-propagating laser beams direction with a level of 7 Gauss/Ampere. The combination of the iodine cell and the solenoid is inserted into a magnetic shield that ensures a residual magnetic field with an attenuation factor of 200. We have observed a linear Zeeman Effect that affects the iodine hyperfine line width as well as its center frequency. We measured large frequency shifts, induced by the longitudinal magnetic field, at the level of 1.8x10-12/Gauss, for all 15 hyperfine components of the R 34[44-0]127 I 2 line at 514.017 nm. Thus an isolation from external magnetic fields below the mG level is required to confer a residual frequency instability at the 10-15 level.