This paper presents a 16-lane, 16-bit complex application-specific instruction processor (ASIP) for baseband processing in massive multiple-input multiple-output (MIMO). The architecture utilizes a 3/4-way very large instruction word (VLIW) with highly efficient pre- and post-processing units specifically trimmed for massive MIMO requirements. Architecture optimizations include features like single cycle vector-dot-product, vector indexing and broadcasting, hardware loops and full complex accumulator to provide high performance for various massive MIMO algorithms. Moreover, the ASIP is fully C-programmable, which is crucial for adapting to the evolving 5G standard. In our evaluation, a full massive MIMO up-link detection is executed in ≈11k clock cycles while synthesis results in ST 28 nm FD-SOI suggest a clock frequency of 900 MHz equating in a detection throughput of 330 Mb/s for a 128×16 massive MIMO system.