The kinesin motor protein Kif1b has previously been implicated in the axonal transport of mitochondria and synaptic vesicles. More recently, KIF1B has been associated with susceptibility to multiple sclerosis (MS). Here we show that Kif1b is required for the localization of mbp (myelin basic protein) mRNA to processes of myelinating oligodendrocytes in zebrafish. We observe the ectopic appearance of myelin-like membrane in kif1b mutants, coincident with the ectopic localization of myelin proteins in kif1b mutant oligodendrocyte cell bodies. These observations suggest that oligodendrocytes localize certain mRNA molecules, namely those encoding small basic proteins such as MBP, to prevent aberrant effects of these proteins elsewhere in the cell. We also find that Kif1b is required for outgrowth of some of the longest axons in the peripheral and central nervous systems. Our data demonstrate previously unknown functions of kif1b in vivo and provide insights into its possible roles in MS.