The resistance of DDM is reducing the current in the circuit so the motor won't run ... You need a clamp meter .. it is not connected to the circuit , but has jaws which clamp around the wire .....
If you can't get one of these , but do have variable power supply you can get a rough idea by first running the motor as it would normally do and note the speed ... then connect the DMM and power motor with variable supply , turn up the voltage till motor runs at same speed as before and read current.