A single-crystal neutron diffraction study of the cubic Laves phase Fe₂Zr at 4.2 K has been made using both polarized and unpolarized incident beams. The samples were prepared from high-purity zirconium and iron and exhibited resistance ratios (_{rho 293} _K/_{rho 4.2 K}) of typically 95, indicative of samples with good long-range order and homogeneity. The material has a Curie temperature of 604(2) K and a cell dimension of a=7.063(1) AA at ambient temperature in agreement with previous measurements for this composition by others. The saturation magnetization of 3.46(1) mu _B/formula unit at 4.2 K is higher than previously observed. The magnetization density of the sample has been fitted by a weighted least-squares procedure to a multipole model of the iron moment based on free-atom wavefunctions for Fe²⁺. The symmetry at the iron site is 3m and the independent symmetry-allowed multipoles up to l=4 are Y₀₀, Y₂₀, Y₄₀ and Y_43-: these have amplitudes 2.11(3), 0.03(2), 0.16(4) and -0.30(4) mu _B respectively. The magnetization at the Zr site is negative and is modelled by a single spherical term, Y₀₀=-0.32(5) mu _B. The remaining magnetization of -0.44 mu _B/formula unit is associated with diffuse density. These findings are discussed in the light of band structure calculations and previous studies of magnetic Laves phases.