diff --git a/lib/rules/jsx-curly-brace-presence.js b/lib/rules/jsx-curly-brace-presence.js
index a4f1dbdc64..40030279b0 100755
--- a/lib/rules/jsx-curly-brace-presence.js
+++ b/lib/rules/jsx-curly-brace-presence.js
@@ -114,26 +114,21 @@ module.exports = {
      * @param {ASTNode} JSXExpressionNode - The AST node with an unnecessary JSX expression
      */
     function reportUnnecessaryCurly(JSXExpressionNode) {
-      const expression = JSXExpressionNode.expression;
-      const expressionType = expression.type;
-      const parentType = JSXExpressionNode.parent.type;
-      const isJSX = jsxUtil.isJSX(expression);
-
-      if (parentType === 'JSXAttribute' && isJSX) {
-        return;
-      }
-
       context.report({
         node: JSXExpressionNode,
         message: 'Curly braces are unnecessary here.',
         fix(fixer) {
+          const expression = JSXExpressionNode.expression;
+          const expressionType = expression.type;
+          const parentType = JSXExpressionNode.parent.type;
+
           let textToReplace;
           if (parentType === 'JSXAttribute') {
             textToReplace = `"${expressionType === 'TemplateLiteral' ?
               expression.quasis[0].value.raw :
               expression.raw.substring(1, expression.raw.length - 1)
             }"`;
-          } else if (isJSX) {
+          } else if (jsxUtil.isJSX(expression)) {
             const sourceCode = context.getSourceCode();
 
             textToReplace = sourceCode.getText(expression);
@@ -244,6 +239,20 @@ module.exports = {
     }
 
     function shouldCheckForUnnecessaryCurly(parent, node, config) {
+      // Bail out if the parent is a JSXAttribute & its contents aren't
+      // StringLiteral or TemplateLiteral since e.g
+      // <App prop1={<CustomEl />} prop2={<CustomEl>...</CustomEl>} />
+
+      if (
+        parent.type && parent.type === 'JSXAttribute' &&
+        (node.expression && node.expression.type &&
+          node.expression.type !== 'Literal' &&
+          node.expression.type !== 'StringLiteral' &&
+          node.expression.type !== 'TemplateLiteral')
+      ) {
+        return false;
+      }
+
       // If there are adjacent `JsxExpressionContainer` then there is no need,
       // to check for unnecessary curly braces.
       if (jsxUtil.isJSX(parent) && hasAdjacentJsxExpressionContainers(node, parent.children)) {