Use this circuit instead
(relay driver)
https://pradhap87.blogspot.com.ar/2010/01/relay-lockun-lock-unit.html
just replace the relay coil with the motor.
The circuit that you are using (figure 1) is going to be always ON unless the input voltage is near the supply voltage.
The arduino delivers +5volts at the most. So the arduino will not be able to turn it OFF. Unless you use an open collector output.
Fig 2 is ok but add the diode in parallel with the motor that is included in my link, to protect the transistor.
Hope that this helps