The conduction electrons in a metal experience competing interactions with each other and the atomic nuclei. This competition can lead to many types of magnetic order in metals. For example, in chromium the electrons order to form a spin-density-wave (SDW) antiferromagnetic state. A magnetic field may be used to perturb or tune materials with delicately balanced electronic interactions. Here, we show that the application of a magnetic field can induce SDW magnetic order in a quasi-2D metamagnetic metal, where none exists in the absence of the field. We use magnetic neutron scattering to show that the application of a large (B ≈ 8 T) magnetic field to the perovskite metal Sr3Ru2O7 (refs 3-7) can be used to tune the material through two magnetically ordered SDW states. The ordered states exist over relatively small ranges in field (≲0.4 T), suggesting that their origin is due to a new mechanism related to the electronic fine structure near the Fermi energy, possibly combined with the stabilizing effect of magnetic fluctuations. The magnetic field direction is shown to control the SDW domain populations, which naturally explains the strong resistivity anisotropy or 'electronic nematic' behaviour observed in this material.