It depends more on current than on voltage.
If it's a small motor, and i presume it is if it can run from a single AA battery, then you can use many different transistors.
If you get a TIP120 transistor then you should be on the safe side even if the motor is not very small.
This should help you get along (second schematic from the top) :
The diode in the schematic is very important as it protects your Arduino from so called back emf spikes that occur when the motor stops running.
Hope this helps a bit