Garey and Johnson, page 214, $K$th Shortest Path:
Given a graph $G=(V,E)$, a positive integer length for each edge, specified vertices $s,t$, and positive integers $B,K$, the question whether there are $K$ or more distinct simple paths from $s$ to $t$ each of length $B$ or less, is not even known to be in NP.
This doesn't quite answer your question, since it does not require the paths to be vertex-disjoint, but it may show you where to start looking.
See also page 217, Maximum Length-Bounded Disjoint Paths: given a graph, two specified vertices, and two positive integers $J,K$, does the graph have $J$ or more mutually vertex-disjoint paths joining the vertices, none involving more than $K$ edges. This one is NP-complete, and actually looks more relevant than the first one.