We develop a small open economy model with nominal rigidities and fragmented labor markets to study the response of the monetary policy to a migration shock. Migrants are characterized by their productivity levels, their restrictions to accumulate capital, as well as by the flexibility of their labor income. Our results show that the monetary policy response depends on the characteristics of migrants and the local labor market. An inflow of low(high)-productivity workers reduces(increases) marginal costs, lowers(raises) inflation expectations and pushes the Central Bank to reduce(increase) the interest rate. The model is calibrated to the Colombian economy and used to analyze a migratory inflow of financially constraint workers from Venezuela into a sector with flexible and low wages.

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