diff --git a/packages/formatjs/__tests__/wasm.test.ts b/packages/formatjs/__tests__/wasm.test.ts
index 29780795a..87cca20a7 100644
--- a/packages/formatjs/__tests__/wasm.test.ts
+++ b/packages/formatjs/__tests__/wasm.test.ts
@@ -609,4 +609,63 @@ describe("formatjs swc plugin", () => {
     expect(code2).toMatch(/id: "Ae\/S0P"/);
     expect(code3).toMatch(/id: "Ae\/S0P"/);
   });
+
+  it("should not error on valid JSX outside formatjs calls (issue #588)", async () => {
+    // Member expression JSX names like React.Suspense with JSX fallback props
+    // should not trigger the static evaluation error.
+    const input = `
+      import React from 'react';
+
+      const Loading = () => <div>Loading...</div>;
+
+      function App() {
+        return (
+          <React.Suspense fallback={<Loading />}>
+            <div>Content</div>
+          </React.Suspense>
+        );
+      }
+    `;
+
+    // Should succeed without throwing "must be statically evaluate-able" error
+    await expect(transformCode(input)).resolves.toBeDefined();
+  });
+
+  it("should not error on conditional JSX outside formatjs calls", async () => {
+    // Conditional JSX expressions unrelated to formatjs should not be evaluated
+    const input = `
+      import React from 'react';
+
+      function App({ isLoading }: { isLoading: boolean }) {
+        return (
+          <div>
+            {isLoading ? <span>Loading...</span> : <span>Done</span>}
+          </div>
+        );
+      }
+    `;
+
+    await expect(transformCode(input)).resolves.toBeDefined();
+  });
+
+  it("should not error on FormattedMessage with JSX values prop", async () => {
+    // FormattedMessage with a `values` prop containing JSX should not error,
+    // since `values` is not a known formatjs descriptor key.
+    const input = `
+      import React from 'react';
+      import { FormattedMessage } from 'react-intl';
+
+      function App() {
+        return (
+          <FormattedMessage
+            defaultMessage="Hello <b>{name}</b>"
+            values={{ b: (chunks) => <b>{chunks}</b>, name: "World" }}
+          />
+        );
+      }
+    `;
+
+    const output = await transformCode(input);
+    expect(output).toMatch(/defaultMessage/);
+  });
 });
diff --git a/packages/formatjs/transform/src/lib.rs b/packages/formatjs/transform/src/lib.rs
index 42424290c..4450c2453 100644
--- a/packages/formatjs/transform/src/lib.rs
+++ b/packages/formatjs/transform/src/lib.rs
@@ -91,9 +91,17 @@ impl MessageDescriptorExtractor for JSXAttrOrSpread {
             let key = match name {
                 JSXAttrName::Ident(name)
                 | JSXAttrName::JSXNamespacedName(JSXNamespacedName { name, .. }) => {
-                    Some(name.sym.to_string())
+                    name.sym.to_string()
                 }
             };
+
+            // Only evaluate values for known formatjs message descriptor keys.
+            // Attributes like `values`, `fallback`, etc. may contain JSX
+            // expressions that cannot (and should not) be statically evaluated.
+            if !matches!(key.as_str(), "id" | "defaultMessage" | "description") {
+                return None;
+            }
+
             let value = match value {
                 JSXAttrValue::Str(s) => Some(MessageDescriptionValue::Str(
                     s.value.as_str().expect("non-utf8 string").to_string(),
@@ -126,7 +134,7 @@ impl MessageDescriptorExtractor for JSXAttrOrSpread {
                 _ => None,
             };
 
-            if let (Some(key), Some(value)) = (key, value) {
+            if let Some(value) = value {
                 Some((key, value))
             } else {
                 None
@@ -978,10 +986,17 @@ impl<'a, C: Clone + Comments, S: SourceMapper> VisitMut for FormatJSVisitor<'a,
 
         let name = &jsx_opening_elem.name;
 
-        if let JSXElementName::Ident(ident) = name {
-            if !self.component_names.contains(&*ident.sym) {
-                return;
+        // Only process known formatjs component names (simple identifiers).
+        // Member expressions (e.g. `React.Suspense`) and namespaced names are
+        // never formatjs components, so return early to avoid evaluating their
+        // attributes.
+        match name {
+            JSXElementName::Ident(ident) => {
+                if !self.component_names.contains(&*ident.sym) {
+                    return;
+                }
             }
+            _ => return,
         }
 
         let mut descriptor = self.create_message_descriptor_from_extractor(&jsx_opening_elem.attrs);