Minimal wall thickness varies depending on the 3D printing machine used and the material chosen for the part. For the printer, if you choose extrusion-based 3D printing, your possible dimensions will depend on nozzle size. For powder-based 3D printing, the size of the laser beam will partly determine minimum size, as will the size of the powder particles.
Also, for extrusion based printers, the layer method of building a part means very small features easily deform or detach because there is insufficient material to connect to the body of the part.
Another issue is post processing. During this stage, the thin wall can easily be damaged during cleaning or support material removal.
Several printers can print thicknesses of 1 mm. As shown in this chart from Fictiv, you can go lower, but few manufacturers or service bureaus recommend that if you want a successful build.