The short answer is yes. Have a look at sequential MCMC/ particle filters.
Essentially, your prior consists of a bunch of particles ($M$). So to sample from your prior, just select a particle with probability $1/M$. Since each particle has equal probability of being chosen, this term disappears in the M-H ratio.
A big problem with particle filters is particle degeneracy. This happens because you are trying to represent a continuous distribution with discrete particles - there's no such thing as a free lunch!
Clarification for Srikant Vadali
The question as I read it is: I have output, i.e. posterior from a MCMC scheme. I want to use this posterior as a prior for a new data set.
This (probably) means that you have a discrete representation of a continuous distribution, i.e. a particle representation. So rather than doing a random walk on a continous distribution (say), you need to pick values from your prior, i.e. you pick a particle.
Toni et al., use this idea with ABC.