Unlike mammals, adult zebrafish undergo spontaneous recovery after major spinal cord injury. Whereas reactive gliosis presents a roadblock for mammalian spinal cord repair, glial cells in zebrafish elicit pro-regenerative bridging functions after injury. Here, we perform genetic lineage tracing, assessment of regulatory sequences and inducible cell ablation to define mechanisms that direct the molecular and cellular responses of glial cells after spinal cord injury in adult zebrafish. Using a newly generated CreERT2 transgenic line, we show that the cells directing expression of the bridging glial marker ctgfa give rise to regenerating glia after injury, with negligible contribution to either neuronal or oligodendrocyte lineages. A 1 kb sequence upstream of the ctgfa gene was sufficient to direct expression in early bridging glia after injury. Finally, ablation of ctgfa-expressing cells using a transgenic nitroreductase strategy impaired glial bridging and recovery of swim behavior after injury. This study identifies key regulatory features, cellular progeny, and requirements of glial cells during innate spinal cord regeneration.