Hubble is in space. They just pointed it somewhere and said “don’t move” (well, multiple times and stacked, but the effect is the same). The galaxies themselves are so far away their own motion is way less than a single pixel.
The motion of Hubble (and basically everything inside the Milky Way) relative to the galaxies in that picture is ~250,000 km/s, or 0.83 c.
At this speed, it would take ~100,000 years for the galaxy to move its own length, and even then the movement would be in a direction which doesn’t cause much blur.
http://www.wolframalpha.com/input/?i=12e9%20light%20years%20...