diff --git a/src/expr/core/src/expr/expr_udf.rs b/src/expr/core/src/expr/expr_udf.rs
index ccd7a6ed70fd3..0c67dc3c58df1 100644
--- a/src/expr/core/src/expr/expr_udf.rs
+++ b/src/expr/core/src/expr/expr_udf.rs
@@ -51,9 +51,13 @@ pub struct UserDefinedFunction {
     identifier: String,
     span: await_tree::Span,
     /// Number of remaining successful calls until retry is enabled.
+    /// This parameter is designed to prevent continuous retry on every call, which would increase delay.
+    /// Logic:
+    /// It resets to INITIAL_RETRY_COUNT after a single failure and then decrements with each call, enabling retry when it reaches zero.
     /// If non-zero, we will not retry on connection errors to prevent blocking the stream.
     /// On each connection error, the count will be reset to `INITIAL_RETRY_COUNT`.
     /// On each successful call, the count will be decreased by 1.
+    /// Link:
     /// See <https://github.com/risingwavelabs/risingwave/issues/13791>.
     disable_retry_count: AtomicU8,
     /// Always retry. Overrides `disable_retry_count`.
@@ -152,7 +156,11 @@ impl UserDefinedFunction {
                 let disable_retry_count = self.disable_retry_count.load(Ordering::Relaxed);
                 let result = if self.always_retry_on_network_error {
                     client
-                        .call_with_always_retry_on_network_error(&self.identifier, arrow_input)
+                        .call_with_always_retry_on_network_error(
+                            &self.identifier,
+                            arrow_input,
+                            &fragment_id,
+                        )
                         .instrument_await(self.span.clone())
                         .await
                 } else {
diff --git a/src/expr/udf/src/external.rs b/src/expr/udf/src/external.rs
index cb33d289c35b0..b7439f07f86b8 100644
--- a/src/expr/udf/src/external.rs
+++ b/src/expr/udf/src/external.rs
@@ -30,6 +30,7 @@ use thiserror_ext::AsReport;
 use tokio::time::Duration as TokioDuration;
 use tonic::transport::Channel;
 
+use crate::metrics::GLOBAL_METRICS;
 use crate::{Error, Result};
 
 // Interval between two successive probes of the UDF DNS.
@@ -182,8 +183,11 @@ impl ArrowFlightUdfClient {
         &self,
         id: &str,
         input: RecordBatch,
+        fragment_id: &str,
     ) -> Result<RecordBatch> {
         let mut backoff = Duration::from_millis(100);
+        let metrics = &*GLOBAL_METRICS;
+        let labels: &[&str; 4] = &[&self.addr, "external", &id, &fragment_id];
         loop {
             match self.call(id, input.clone()).await {
                 Err(err) if err.is_tonic_error() => {
@@ -196,6 +200,7 @@ impl ArrowFlightUdfClient {
                     return ret;
                 }
             }
+            metrics.udf_failure_count.with_label_values(labels).inc();
             tokio::time::sleep(backoff).await;
             backoff *= 2;
         }