Motors are great electrical noise generators, especially when they start and stop. The electrical noise is both radiated through the air and conducted back down the mains. The extent of each type of noise depends on the type of motor and if it used some sort of electronic speed control.
For a simple AC induction motor or 'universal' motor you may be able to get by with plugging the motor into a different mains circuit. Ideally you would want to stop the noise at its source though. The motor itself generates noise and I like to say the first line of defense is to put a line filter on the mains feed to the motor as close to the motor as possible. Here is an example of the type of filters I use for small AC motors:
http://www.soigeneris.com/line_filter_kit-details.aspx (this is my website and I am not posting this as advertising, it is just the easiest link for me to find and post).
Filtering the AC input to other devices that might be affected is the next line of defense. In my small shop I also used one of these type of filters on the mains going to my shop PC after finding that a small florescent lamp above the workbench would generate enough noise to cause the 5V on the USB bus to go negative briefly.
You can find these types of filters inside a lot of different types of equipment so even if it is hard to source in your country or you need one quickly you might be able to salvage one from an old photo copier, etc.