What does a cross section look like? I am suspecting you could maybe rip some pre-finished oak quarter round to fill your gap. Use some adhesive to hold it in place.
Here is a guess as to the cross section. Blue represents the seal. Blue is wood, which looks like it may have a contrasting bevel on its edge. I presume your photo was taken with the door open.
For just noise, you could stuff some foam weather stripping in deep enough that it would not be noticeable from the kitchen. You could maybe rip something like
http://www.homedepot.com/p/MD-Build...tripping-for-Air-Conditioners-02006/100353462 to size. An electric knife is a good tool for cutting such foam, but scissors would probably work OK. The compression would hide your ragged cut.
You could also look into noise absorbing materials for increased sound attenuation.
I wonder if a gap could important for ventilation.