I plotted my kmer histogram generated by jellyfish and tried fitting it to the poisson distribution. What could be the probable reason for a shift to the right?

Please provide context. What are you trying to do?

Poisson distributions can take various forms, by the way, and they differ based on the value of Lambda (λ). Both of your curves look Poison-like to me.

I guess the black curve is the actual kmer distribution, and the dashed green is the fitted poisson? I will assume yes:

The tails of your kmer distribution do not fit a poisson, and in particular, the peak of erroneous kmers is probably what is skewing the fitted distribution to the left.

Please provide context. What are you trying to do?

Poisson distributions can take various forms, by the way, and they differ based on the value of Lambda (λ). Both of your curves look Poison-like to me.