diff --git a/build_tools/azure/install.sh b/build_tools/azure/install.sh
index 1c76a7a4aa5d3..3bbc4b07a6f57 100755
--- a/build_tools/azure/install.sh
+++ b/build_tools/azure/install.sh
@@ -104,6 +104,12 @@ scikit_learn_install() {
         # Without openmp, we use the system clang. Here we use /usr/bin/ar
         # instead because llvm-ar errors
         export AR=/usr/bin/ar
+        # Make sure omp.h is not present in the conda environment, so that
+        # using an unprotected "cimport openmp" will make this build fail. At
+        # the time of writing (2023-01-13), on OSX, blas (mkl or openblas)
+        # brings in openmp so that you end up having the omp.h include inside
+        # the conda environment.
+        find $CONDA_PREFIX -name omp.h -delete -print
     fi
 
     if [[ "$UNAMESTR" == "Linux" ]]; then