diff --git a/datafusion/optimizer/src/eliminate_group_by_constant.rs b/datafusion/optimizer/src/eliminate_group_by_constant.rs
index e21241ba7d993..e3a75b64d5f11 100644
--- a/datafusion/optimizer/src/eliminate_group_by_constant.rs
+++ b/datafusion/optimizer/src/eliminate_group_by_constant.rs
@@ -64,10 +64,10 @@ impl OptimizerRule for EliminateGroupByConstant {
                     .group_expr
                     .iter()
                     .partition(|expr| is_redundant_group_expr(expr, &group_by_columns));
+                // Only eliminate when at least one required group expression remains. A grouping
+                // aggregate emits 0 rows on empty input; a global aggregate emits 1 NULL row.
 
-                if redundant.is_empty()
-                    || (required.is_empty() && aggregate.aggr_expr.is_empty())
-                {
+                if redundant.is_empty() || required.is_empty() {
                     return Ok(Transformed::no(LogicalPlan::Aggregate(aggregate)));
                 }
 
@@ -228,9 +228,8 @@ mod tests {
             .build()?;
 
         assert_optimized_plan_equal!(plan, @r#"
-        Projection: Utf8("test"), UInt32(123), count(test.c)
-          Aggregate: groupBy=[[]], aggr=[[count(test.c)]]
-            TableScan: test
+        Aggregate: groupBy=[[Utf8("test"), UInt32(123)]], aggr=[[count(test.c)]]
+          TableScan: test
         "#)
     }
 
diff --git a/datafusion/sqllogictest/test_files/aggregate.slt b/datafusion/sqllogictest/test_files/aggregate.slt
index 70acff3cb7b9a..fdb4b33e93069 100644
--- a/datafusion/sqllogictest/test_files/aggregate.slt
+++ b/datafusion/sqllogictest/test_files/aggregate.slt
@@ -7842,6 +7842,23 @@ CREATE TABLE t1(v1 int);
 statement error DataFusion error: Error during planning: Aggregate functions are not allowed in the WHERE clause. Consider using HAVING instead
 SELECT v1 FROM t1 WHERE ((count(v1) % 1) << 1) > 0;
 
+# issue: https://github.com/apache/datafusion/issues/11748
+query R
+SELECT AVG(v1) FROM t1 GROUP BY false HAVING false;
+----
+
+query R
+SELECT AVG(v1) FROM t1 GROUP BY false;
+----
+
+statement ok
+INSERT INTO t1 VALUES (1), (2), (3);
+
+query R
+SELECT AVG(v1) FROM t1 GROUP BY false;
+----
+2
+
 statement ok
 DROP TABLE t1;
 
diff --git a/datafusion/sqllogictest/test_files/optimizer_group_by_constant.slt b/datafusion/sqllogictest/test_files/optimizer_group_by_constant.slt
index da1e7de22bb7a..9df55512413f3 100644
--- a/datafusion/sqllogictest/test_files/optimizer_group_by_constant.slt
+++ b/datafusion/sqllogictest/test_files/optimizer_group_by_constant.slt
@@ -60,10 +60,9 @@ FROM test_table t
 group by 1, 2, 3
 ----
 logical_plan
-01)Projection: Int64(123), Int64(456), Int64(789), count(Int64(1)), avg(t.c12)
-02)--Aggregate: groupBy=[[]], aggr=[[count(Int64(1)), avg(t.c12)]]
-03)----SubqueryAlias: t
-04)------TableScan: test_table projection=[c12]
+01)Aggregate: groupBy=[[Int64(123), Int64(456), Int64(789)]], aggr=[[count(Int64(1)), avg(t.c12)]]
+02)--SubqueryAlias: t
+03)----TableScan: test_table projection=[c12]
 
 query TT
 EXPLAIN 
@@ -72,8 +71,8 @@ FROM test_table t
 GROUP BY 1, 2
 ----
 logical_plan
-01)Projection: Date32("2023-05-04") AS dt, Boolean(true) AS today_filter, count(Int64(1))
-02)--Aggregate: groupBy=[[]], aggr=[[count(Int64(1))]]
+01)Projection: to_date(Utf8("2023-05-04")) AS dt, date_part(Utf8("DAY"),now()) < Int64(1000) AS today_filter, count(Int64(1))
+02)--Aggregate: groupBy=[[Date32("2023-05-04") AS to_date(Utf8("2023-05-04")), Boolean(true) AS date_part(Utf8("DAY"),now()) < Int64(1000)]], aggr=[[count(Int64(1))]]
 03)----SubqueryAlias: t
 04)------TableScan: test_table projection=[]
 
@@ -90,10 +89,9 @@ FROM test_table t
 GROUP BY 1
 ----
 logical_plan
-01)Projection: Boolean(true) AS NOT date_part(Utf8("MONTH"),now()) BETWEEN Int64(50) AND Int64(60), count(Int64(1))
-02)--Aggregate: groupBy=[[]], aggr=[[count(Int64(1))]]
-03)----SubqueryAlias: t
-04)------TableScan: test_table projection=[]
+01)Aggregate: groupBy=[[Boolean(true) AS NOT date_part(Utf8("MONTH"),now()) BETWEEN Int64(50) AND Int64(60)]], aggr=[[count(Int64(1))]]
+02)--SubqueryAlias: t
+03)----TableScan: test_table projection=[]
 
 query TT
 EXPLAIN 
@@ -119,7 +117,7 @@ logical_plan
 
 # Config reset
 
-# The SLT runner sets `target_partitions` to 4 instead of using the default, so 
+# The SLT runner sets `target_partitions` to 4 instead of using the default, so
 # reset it explicitly.
 statement ok
 set datafusion.execution.target_partitions = 4;