We report on the effect of a weak magnetic field applied on an iodine cell used to frequency stabilize a laser. A 1.5 μ m laser is frequency tripled in order to excite the molecular transitions at 0.51 μ m and frequency locked on a hyperfine line. With this frequency reference, we report short-term stability about 3 × 10 - 14 τ - 1 / 2 , with a minimum value of 4 × 10 - 15 at 200 s. The lower part of 10 - 15 frequency stability domain is reached, in our case, only by adding an efficient magnetic shield around the sealed quartz iodine cell. In order to quantify the Zeeman effect, we applied magnetic fields of several × 10 - 4  T on the cell containing the iodine vapour. The Zeeman effect affects the lineshape transition in such a way that we observe a modification of the laser frequency. We have measured this linear Zeeman shift at ( 1062 ± 6 ) × 10 4  Hz/T for the a 1 hyperfine component of the R(34) 44-0 transition, near 514 nm by applying a magnetic field along the cell. Thus, in case of uncontrolled magnetic fields of an order of magnitude of 1 × 10 - 4  T, the frequency stability is limited in the upper of the 10 - 14 domain.