diff --git a/ci/travis_script_python.sh b/ci/travis_script_python.sh
index a487da596bd..9ed5825bb8f 100755
--- a/ci/travis_script_python.sh
+++ b/ci/travis_script_python.sh
@@ -43,11 +43,14 @@ conda install -y -q pip \
       pandas \
       cython
 
-if [ "$PYTHON_VERSION" != "2.7" ] || [ $TRAVIS_OS_NAME != "osx" ]; then
-  # Install pytorch for torch tensor conversion tests
-  # PyTorch seems to be broken on Python 2.7 on macOS so we skip it
-  conda install -y -q pytorch torchvision -c soumith
-fi
+# ARROW-2093: PyTorch increases the size of our conda dependency stack
+# significantly, and so we have disabled these tests in Travis CI for now
+
+# if [ "$PYTHON_VERSION" != "2.7" ] || [ $TRAVIS_OS_NAME != "osx" ]; then
+#   # Install pytorch for torch tensor conversion tests
+#   # PyTorch seems to be broken on Python 2.7 on macOS so we skip it
+#   conda install -y -q pytorch torchvision -c soumith
+# fi
 
 # Build C++ libraries
 mkdir -p $ARROW_CPP_BUILD_DIR