  The odd colouring number is a new graph parameter introduced by
Petru\v{s}evski and \v{S}krekovski. In this note, we show that graphs with so
called product structure have bounded odd-colouring number. By known results on
the product structure of $k$-planar graphs, this implies that $k$-planar graphs
have bounded odd-colouring number, which answers a question of Cranston,
Lafferty, and Song.
