Not sure about the actual ground clearance, but it's low because the original low-bypass engines on the -100 and -200 models which were mounted underneath the wings had a short enough diameter where the ground clearance could be low. However, when the larger turbofans mounted on struts under the wings were introduced on the -300 and above; they had to flatten out the bottom of the engine nacelles due to the low ground clearance. Also, when the 737 was introduced it shared a similar fuselage cross section with the 727, which had the same cross section as the 707, and with rear-mounted engines ground clearance isn't much of a problem.
Look at any photo of a 737 (or 727 or 707 for that matter) and you'll see just how low to the ground it is. And if you really want to get the full effect; play Cheech and Chong's "Low Rider" music in the background...
Ya I suppose that sentence had a bit too much info in it; the rear-mounted engines was referring to the 727; I only mentioned the 707 as the predecessor to the 727 and how they shared a similar fuselage. Of course, the 707's engines were mounted underneath the wings, but being low-bypass rather than turbofans ground clearance wasn't much of an issue for that plane either.
And apparently, I also should have paid closer attention to jhagan's question, too, which was about the ground clearance of the 777 engine and not the 737. I'd say it's normal in that picture; just the shear size of the thing is what makes it look like it's hanging kinda low.