We report that long double-stranded DNA confined to quasi-1D nanochannels undergoes superdiffusive motion under the action of the enzyme T4 DNA ligase in the presence of necessary co-factors. Inside the confined environment of the nanochannel, double-stranded DNA molecules stretch out due to self-avoiding interactions. In absence of a catalytically active enzyme, we see classical diffusion of the center of mass. However, cooperative interactions of proteins with the DNA can lead to directed motion of DNA molecules inside the nanochannel. Here we show directed motion in this configuration for three different proteins (T4 DNA ligase, MutS, E. coli DNA ligase) in the presence of their energetic co-factors (ATP, NAD+).