diff --git a/.changeset/wild-suns-beg.md b/.changeset/wild-suns-beg.md
new file mode 100644
index 0000000000..845cf14fe8
--- /dev/null
+++ b/.changeset/wild-suns-beg.md
@@ -0,0 +1,6 @@
+---
+"@pnpm/modules-cleaner": patch
+"pnpm": patch
+---
+
+Installation should not fail if an empty `node_modules` directory cannot be removed [#7405](https://github.com/pnpm/pnpm/issues/7405).
diff --git a/pkg-manager/modules-cleaner/src/prune.ts b/pkg-manager/modules-cleaner/src/prune.ts
index 94feb952da..75f97791b8 100644
--- a/pkg-manager/modules-cleaner/src/prune.ts
+++ b/pkg-manager/modules-cleaner/src/prune.ts
@@ -114,7 +114,12 @@ export async function prune (
       })
     }))
     await Promise.all(Array.from(removedFromScopes).map((scope) => removeIfEmpty(path.join(modulesDir, scope))))
-    await removeIfEmpty(modulesDir)
+    try {
+      await removeIfEmpty(modulesDir)
+    } catch {
+      // On some server setups we might not have permission to remove the node_modules directory.
+      // That's fine, just proceed.
+    }
   }))
 
   const selectedImporterIds = importers.map((importer) => importer.id).sort()