diff --git a/src/tint/lang/wgsl/ir_roundtrip_test.cc b/src/tint/lang/wgsl/ir_roundtrip_test.cc
index f75a7a0c2c..49c7b51222 100644
--- a/src/tint/lang/wgsl/ir_roundtrip_test.cc
+++ b/src/tint/lang/wgsl/ir_roundtrip_test.cc
@@ -3401,6 +3401,16 @@ fn a(x : f32) {
 )");
 }
 
+// Test that we do not try to name the unnameable builtin structure types in nested array
+// declarations. See crbug.com/380898799.
+TEST_F(IRToProgramRoundtripTest, BuiltinStructInInferredNestedArrayType) {
+    RUN_TEST(R"(
+fn a(x : f32) {
+  let y = array(array(frexp(x)));
+}
+)");
+}
+
 // Test that we rename declarations that shadow builtin types when they are used in arrays.
 // See crbug.com/380903161.
 TEST_F(IRToProgramRoundtripTest, BuiltinTypeNameShadowedAndUsedInArray) {
diff --git a/src/tint/lang/wgsl/writer/ir_to_program/ir_to_program.cc b/src/tint/lang/wgsl/writer/ir_to_program/ir_to_program.cc
index bf59be31fe..56ae2c3c94 100644
--- a/src/tint/lang/wgsl/writer/ir_to_program/ir_to_program.cc
+++ b/src/tint/lang/wgsl/writer/ir_to_program/ir_to_program.cc
@@ -988,12 +988,12 @@ class State {
                 }
             },
             [&](const core::type::Array* a) {
-                auto el = Type(a->ElemType());
-                if (!el) {
+                if (ContainsBuiltinStruct(a)) {
                     // The element type is untypeable, so we need to infer it instead.
                     return ast::Type{b.Expr(b.Ident("array"))};
                 }
 
+                auto el = Type(a->ElemType());
                 Vector<const ast::Attribute*, 1> attrs;
                 if (!a->IsStrideImplicit()) {
                     attrs.Push(b.Stride(a->Stride()));
@@ -1053,8 +1053,7 @@ class State {
 
     ast::Type Struct(const core::type::Struct* s) {
         // Skip builtin structures.
-        // TODO(350778507): Consider using a struct flag for builtin structures instead.
-        if (tint::HasPrefix(s->Name().NameView(), "__")) {
+        if (ContainsBuiltinStruct(s)) {
             return ast::Type{};
         }
 
@@ -1108,6 +1107,20 @@ class State {
         return b.ty(n);
     }
 
+    bool ContainsBuiltinStruct(const core::type::Type* ty) {
+        if (auto* s = ty->As<core::type::Struct>()) {
+            // Note: We don't need to check the members of the struct, as builtin structures cannot
+            // be nested inside other structures.
+            // TODO(350778507): Consider using a struct flag for builtin structures instead.
+            if (tint::HasPrefix(s->Name().NameView(), "__")) {
+                return true;
+            }
+        } else if (auto* a = ty->As<core::type::Array>()) {
+            return ContainsBuiltinStruct(a->ElemType());
+        }
+        return false;
+    }
+
     ////////////////////////////////////////////////////////////////////////////////////////////////
     // Bindings
     ////////////////////////////////////////////////////////////////////////////////////////////////