diff --git a/ci/docker/conda.dockerfile b/ci/docker/conda.dockerfile
index 4b497b47036..6492e761fdd 100644
--- a/ci/docker/conda.dockerfile
+++ b/ci/docker/conda.dockerfile
@@ -30,9 +30,11 @@ RUN export DEBIAN_FRONTEND=noninteractive && \
     apt-get clean && \
     rm -rf /var/lib/apt/lists/*
 
-# install conda and mamba via miniforge
+# Install conda and mamba via miniforge.
+# Temporarily pin to an old version of miniforge due to a regression in the mamba solver.
+# See https://github.com/apache/arrow/issues/49998.
 COPY ci/scripts/install_conda.sh /arrow/ci/scripts/
-RUN /arrow/ci/scripts/install_conda.sh miniforge3 latest /opt/conda
+RUN /arrow/ci/scripts/install_conda.sh miniforge3 26.1.1-3 /opt/conda
 ENV PATH=/opt/conda/bin:$PATH
 
 # create a conda environment
diff --git a/ci/scripts/install_conda.sh b/ci/scripts/install_conda.sh
index c74b318cfa3..ad0965881a3 100755
--- a/ci/scripts/install_conda.sh
+++ b/ci/scripts/install_conda.sh
@@ -30,7 +30,11 @@ installer=$1
 version=$2
 prefix=$3
 
-download_url=https://github.com/conda-forge/miniforge/releases/${version}/download/${installer^}-${platform}-${arch}.sh
+if [ "$version" = "latest" ]; then
+  download_url=https://github.com/conda-forge/miniforge/releases/latest/download/${installer^}-${platform}-${arch}.sh
+else
+  download_url=https://github.com/conda-forge/miniforge/releases/download/${version}/${installer^}-${platform}-${arch}.sh
+fi
 
 echo "Downloading Miniconda installer from ${download_url} ..."