@Wawa: Thanks for pointing out I made a mistake in the Fritzing, the picture below should show the corrected one. Inverted the diode and connected the collector to the cathode of the diode.
Below are pictures of the real setup. The circuit is built six times in parallel to power six pumps (should've tested it more rigorously before soldering it all, but just checked if it worked and not the power) but just the first pump is connected to the circuit. The Fritzing is just a breakdown of the problem. When rebuilding the circuit on a breadboard and powering the motor from the Arduino 5V supply I got the same issue. Powering the motor without the circuit from the Arduino 5V supply works fine.
Complete setup:
Soldered parts:
@jremington: What would you recommend as a motor driver? (shouldn't be too expensive)
@morrisonandboyd: Thank you for enlightening me and explaining all the details! Unfortunately I can't change the supply voltage.
Thanks for all the help so far!