I'm not sure about the MIM Jazz, but I had one on two different basses. The first was a generic Squier PJ bass, and the neck was too thin, I actually had to shim it in to make it tight, before screwing it in. The second was on my Vintage Modified Jazz, and it was just a tad large, and required a bit of sanding to get it to fit, but not much.
BTW, it is for a P Bass, but the size difference in P and Jazz bass necks are typically only at the nut. The heel should be roughly the same. Different Fender lines from different model lines on the other hand seem to have slightly different pockets.
Either way, you can make it fit... And that neck is a great neck. I loved mine. The only thing I recommend is to get the nut slots a little lowered. I found mine was shipped with them a tad high.