A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). The density functions defined by such programs, which may use stochastic branching and recursion, are in general nonparametric, in that they express models on an infinite-dimensional parameter space. However standard inference algorithms usually target distributions with a fixed finite number of parameters. We present the nonparametric involutive Markov chain Monte Carlo (NP-iMCMC) framework for designing MCMC inference algorithms for nonparametric models expressible in a universal PPL. Building on the unifying involutive MCMC framework, we show how a wide range of MCMC algorithms (including Metropolis-Hasting, Gibbs sampling and Hamiltonian Monte Carlo) can be systematically generalised to nonparametric models, and presented as particular instantiations of the NP-iMCMC framework. Such a unifying framework makes it easy to derive and prove the correctness of new nonparametric extensions of existing MCMC algorithms. Preliminary empirical results suggest that strengths of the MCMC algorithms carry onto its nonparametric extension. Moreover, a recent empirical study on nonparametric HMC, which is an instance of NP-iMCMC, has demonstrated significant performance improvements over existing general MCMC approaches.