diff --git a/modules/reindex/build.gradle b/modules/reindex/build.gradle
index 31fbc3ca1f64e..ca2b6e474a6b7 100644
--- a/modules/reindex/build.gradle
+++ b/modules/reindex/build.gradle
@@ -95,6 +95,11 @@ dependencies {
   es090 'org.elasticsearch:elasticsearch:0.90.13@zip'
 }
 
+// Issue tracked in https://github.com/elastic/elasticsearch/issues/40904
+if (project.inFipsJvm) {
+  integTest.enabled = false
+}
+
 if (Os.isFamily(Os.FAMILY_WINDOWS)) {
   logger.warn("Disabling reindex-from-old tests because we can't get the pid file on windows")
   integTest.runner {