--- a/log4j-layout-template-json/src/main/java/org/apache/logging/log4j/layout/template/json/util/JsonWriter.java	2026-04-14 14:24:27.336457199 +0200
+++ b/log4j-layout-template-json/src/main/java/org/apache/logging/log4j/layout/template/json/util/JsonWriter.java	2026-04-14 14:24:45.379955387 +0200
@@ -757,11 +757,21 @@
     }
 
     public void writeNumber(final float number) {
-        stringBuilder.append(number);
+        // Follows the same logic as Jackson's JsonWriteFeature#WRITE_NAN_AS_STRINGS feature.
+        if (!Float.isFinite(number)) {
+            writeString(Float.toString(number));
+        } else {
+            stringBuilder.append(number);
+        }
     }
 
     public void writeNumber(final double number) {
-        stringBuilder.append(number);
+        // Follows the same logic as Jackson's JsonWriteFeature#WRITE_NAN_AS_STRINGS feature.
+        if (!Double.isFinite(number)) {
+            writeString(Double.toString(number));
+        } else {
+            stringBuilder.append(number);
+        }
     }
 
     public void writeNumber(final short number) {