Static program analysis tools can automatically prove many useful properties of programs. However, using static analysis to prove to a third party that a program satisfies a property requires revealing the program's source code. We introduce the concept of zero-knowledge static analysis, in which the prover constructs a zero-knowledge proof about the outcome of the static analysis without revealing the program. We present novel zero-knowledge proof schemes for intra- and inter-procedural abstract interpretation. Our schemes are significantly more efficient than the naive translation of the corresponding static analysis algorithms using existing schemes. We evaluate our approach empirically on real and synthetic programs; with a pairing-based zero knowledge proof scheme as the backend, we are able to prove the control flow analysis on a 2,000-line program in 1,738s. The proof is only 128 bytes and the verification time is 1.4ms. With a transparent zero knowledge proof scheme based on discrete-log, we generate the proof for the tainting analysis on a 12,800-line program in 406 seconds, the proof size is 282 kilobytes, and the verification time is 66 seconds.