diff --git a/lldb/source/Core/ValueObject.cpp b/lldb/source/Core/ValueObject.cpp
--- a/lldb/source/Core/ValueObject.cpp
+++ b/lldb/source/Core/ValueObject.cpp
@@ -2673,7 +2673,10 @@
     // In case of incomplete child compiler type, use the pointee type and try
     // to recreate a new ValueObjectChild using it.
     if (!m_deref_valobj) {
-      if (HasSyntheticValue()) {
+      // FIXME(#59012): C++ stdlib formatters break with incomplete types (e.g.
+      // `std::vector<int> &`). Remove ObjC restriction once that's resolved.
+      if (Language::LanguageIsObjC(GetPreferredDisplayLanguage()) &&
+          HasSyntheticValue()) {
         child_compiler_type = compiler_type.GetPointeeType();
 
         if (child_compiler_type) {
diff --git a/lldb/test/API/lang/cpp/incomplete-stl-types/Makefile b/lldb/test/API/lang/cpp/incomplete-stl-types/Makefile
new file mode 100644
--- /dev/null
+++ b/lldb/test/API/lang/cpp/incomplete-stl-types/Makefile
@@ -0,0 +1,9 @@
+CXX_SOURCES := main.cpp f.cpp
+
+include Makefile.rules
+
+# Force main.cpp to be built with no debug information
+main.o: CFLAGS = $(CFLAGS_NO_DEBUG)
+
+# And force -flimit-debug-info on the rest.
+f.o: CFLAGS_EXTRAS += $(LIMIT_DEBUG_INFO_FLAGS)
diff --git a/lldb/test/API/lang/cpp/incomplete-stl-types/TestStlIncompleteTypes.py b/lldb/test/API/lang/cpp/incomplete-stl-types/TestStlIncompleteTypes.py
new file mode 100644
--- /dev/null
+++ b/lldb/test/API/lang/cpp/incomplete-stl-types/TestStlIncompleteTypes.py
@@ -0,0 +1,18 @@
+"""
+Test situations where the debug info only has a declaration, no definition, for
+an STL container with a formatter.
+"""
+
+import lldb
+from lldbsuite.test.decorators import *
+from lldbsuite.test.lldbtest import *
+from lldbsuite.test import lldbutil
+
+
+class TestStlIncompleteTypes(TestBase):
+    def test(self):
+        self.build()
+        lldbutil.run_to_source_breakpoint(self, "// break here", lldb.SBFileSpec("f.cpp"))
+
+        var = self.frame().GetValueForVariablePath("v")
+        self.assertIn("set", var.GetDisplayTypeName())
diff --git a/lldb/test/API/lang/cpp/incomplete-stl-types/f.cpp b/lldb/test/API/lang/cpp/incomplete-stl-types/f.cpp
new file mode 100644
--- /dev/null
+++ b/lldb/test/API/lang/cpp/incomplete-stl-types/f.cpp
@@ -0,0 +1,5 @@
+#include <set>
+
+void f(std::set<int> &v) {
+  // break here
+}
diff --git a/lldb/test/API/lang/cpp/incomplete-stl-types/main.cpp b/lldb/test/API/lang/cpp/incomplete-stl-types/main.cpp
new file mode 100644
--- /dev/null
+++ b/lldb/test/API/lang/cpp/incomplete-stl-types/main.cpp
@@ -0,0 +1,8 @@
+#include <set>
+
+void f(std::set<int> &v);
+
+int main() {
+  std::set<int> v;
+  f(v);
+}