  Interval minors of bipartite graphs were introduced by Jacob Fox in the study
of Stanley-Wilf limits. Recently, Mohar, Rafiey, Tayfeh-Rezaie and Wu
investigated the maximum number of edges in $K_{k,\ell}$-interval minor free
bipartite graphs when $k=2$ and $k=3$. In this paper, we investigate the
maximum number of edges in $K_{k,\ell}$-interval minor free bipartite graphs
for general $k$ and $\ell$. We also study the maximum number of edges in
$K_{\ell_1,\ell_2,\cdots,\ell_t}$-interval minor free multipartite graphs.
