diff --git a/conda-recipe/meta.yaml b/conda-recipe/meta.yaml
index a6e06f0dfd..812362a627 100644
--- a/conda-recipe/meta.yaml
+++ b/conda-recipe/meta.yaml
@@ -41,6 +41,12 @@ requirements:
         - {{ dep }}
         {% elif dep.startswith('build>=') %}
         - {{ 'python-' ~ dep }}
+        {% elif dep.startswith('cython') %}
+        {% if dep.split(';')[1] == "python_version<'3.13'" %}
+        - {{ dep.split(';')[0] }} # [py<313]
+        {% else %}
+        - {{ dep.split(';')[0] }} # [py>=313]
+        {% endif %}
         {% else %}
         - {{ dep|replace('_','-') }}
         {% endif %}
diff --git a/pyproject.toml b/pyproject.toml
index 1fa466942e..dec9c10ab6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -8,7 +8,8 @@ requires = [
   "scikit-build>=0.17.0",
   "ninja>=1.11.1; platform_system!='Windows'",
   "cmake>=3.29.0",
-  "cython>=3.0.10",
+  "cython>=3.0.10;python_version<'3.13'",
+  "cython>=3.0.10,<3.1.0;python_version>='3.13'",
   "numpy >=1.23",
   # WARNING: check with doc how to upgrade
   "versioneer[toml]==0.29"