diff --git a/docs/changelog/135899.yaml b/docs/changelog/135899.yaml
new file mode 100644
index 0000000000000..680a98a5d6b5e
--- /dev/null
+++ b/docs/changelog/135899.yaml
@@ -0,0 +1,6 @@
+pr: 135899
+summary: Fix date fields sort formatting with missing values
+area: Search
+type: bug
+issues:
+ - 81960
diff --git a/server/src/main/java/org/elasticsearch/search/DocValueFormat.java b/server/src/main/java/org/elasticsearch/search/DocValueFormat.java
index 13256a2481867..31c2659f9d840 100644
--- a/server/src/main/java/org/elasticsearch/search/DocValueFormat.java
+++ b/server/src/main/java/org/elasticsearch/search/DocValueFormat.java
@@ -35,7 +35,12 @@
 import java.text.NumberFormat;
 import java.text.ParseException;
 import java.time.DateTimeException;
+import java.time.Instant;
+import java.time.LocalDate;
+import java.time.LocalDateTime;
+import java.time.LocalTime;
 import java.time.ZoneId;
+import java.time.ZoneOffset;
 import java.util.Arrays;
 import java.util.Base64;
 import java.util.Locale;
@@ -305,6 +310,14 @@ public DateMathParser getDateMathParser() {
 
         @Override
         public String format(long value) {
+            // Handle missing values, represented as Long.MIN_VALUE or Long.MAX_VALUE depending on the sort order
+            if (value == Long.MIN_VALUE) {
+                return formatter.withZone(ZoneOffset.ofHours(0)).format(Instant.EPOCH);
+            } else if (value == Long.MAX_VALUE) {
+                // On descending values, use the maximum possible value for strict_date_time format as the safest option
+                return formatter.withZone(ZoneOffset.ofHours(0)).format(LocalDateTime.of(LocalDate.of(9999, 12, 31), LocalTime.MAX));
+            }
+
             try {
                 return formatter.format(resolution.toInstant(value).atZone(timeZone));
             } catch (DateTimeException dte) {
diff --git a/server/src/test/java/org/elasticsearch/search/DocValueFormatTests.java b/server/src/test/java/org/elasticsearch/search/DocValueFormatTests.java
index 7c9a68cbc91f1..208d837ed7f3b 100644
--- a/server/src/test/java/org/elasticsearch/search/DocValueFormatTests.java
+++ b/server/src/test/java/org/elasticsearch/search/DocValueFormatTests.java
@@ -19,6 +19,7 @@
 import org.elasticsearch.common.io.stream.StreamInput;
 import org.elasticsearch.common.network.InetAddresses;
 import org.elasticsearch.common.time.DateFormatter;
+import org.elasticsearch.common.time.FormatNames;
 import org.elasticsearch.index.mapper.DateFieldMapper.Resolution;
 import org.elasticsearch.index.mapper.RoutingPathFields;
 import org.elasticsearch.index.mapper.TimeSeriesRoutingHashFieldMapper;
@@ -238,6 +239,28 @@ public void testFormatSortFieldOutput() {
         assertThat(dateFormat.formatSortValue(1415580798601L), equalTo("2014-11-10 01:53:18"));
     }
 
+    public void testFormatSortFieldOutputForMissingValues() {
+        DateFormatter formatter = DateFormatter.forPattern(FormatNames.STRICT_DATE_TIME.getName());
+        DocValueFormat.DateTime dateFormat = new DocValueFormat.DateTime(
+            formatter,
+            ZoneOffset.ofHours(randomInt(6)),
+            randomBoolean() ? Resolution.MILLISECONDS : Resolution.NANOSECONDS
+        );
+        dateFormat = (DocValueFormat.DateTime) DocValueFormat.enableFormatSortValues(dateFormat);
+        assertThat(dateFormat.formatSortValue(Long.MIN_VALUE), equalTo("1970-01-01T00:00:00.000Z"));
+        assertThat(dateFormat.formatSortValue(Long.MAX_VALUE), equalTo("9999-12-31T23:59:59.999999999Z"));
+
+        formatter = DateFormatter.forPattern(FormatNames.EPOCH_MILLIS.getName());
+        dateFormat = new DocValueFormat.DateTime(
+            formatter,
+            ZoneOffset.ofHours(randomInt(6)),
+            randomBoolean() ? Resolution.MILLISECONDS : Resolution.NANOSECONDS
+        );
+        dateFormat = (DocValueFormat.DateTime) DocValueFormat.enableFormatSortValues(dateFormat);
+        assertThat(dateFormat.formatSortValue(Long.MIN_VALUE), equalTo("0"));
+        assertThat(dateFormat.formatSortValue(Long.MAX_VALUE), equalTo("253402300799999.999999"));
+    }
+
     public void testBadUtf8() {
         IllegalArgumentException e = expectThrows(
             IllegalArgumentException.class,