diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/ApplyFunctionExpression.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/ApplyFunctionExpression.scala
index 2cee8303dc57b..78f0f8a7af613 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/ApplyFunctionExpression.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/ApplyFunctionExpression.scala
@@ -35,6 +35,7 @@ case class ApplyFunctionExpression(
   override lazy val deterministic: Boolean = function.isDeterministic &&
       children.forall(_.deterministic)
   override def foldable: Boolean = deterministic && children.forall(_.foldable)
+  override def stateful: Boolean = true
 
   private lazy val reusedRow = new SpecificInternalRow(function.inputTypes().toImmutableArraySeq)
 
diff --git a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ApplyFunctionExpressionSuite.scala b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ApplyFunctionExpressionSuite.scala
new file mode 100644
index 0000000000000..9300f107a6aab
--- /dev/null
+++ b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ApplyFunctionExpressionSuite.scala
@@ -0,0 +1,87 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.sql.catalyst.expressions
+
+import java.util.concurrent.{CountDownLatch, TimeUnit}
+
+import scala.concurrent.{ExecutionContext, Future}
+import scala.concurrent.duration._
+
+import org.apache.spark.SparkFunSuite
+import org.apache.spark.sql.catalyst.InternalRow
+import org.apache.spark.sql.connector.catalog.functions.ScalarFunction
+import org.apache.spark.sql.types.{DataType, IntegerType}
+import org.apache.spark.util.ThreadUtils
+
+class ApplyFunctionExpressionSuite extends SparkFunSuite {
+
+  private val intIdentity = new ScalarFunction[Int] {
+    override def inputTypes(): Array[DataType] = Array(IntegerType)
+    override def resultType(): DataType = IntegerType
+    override def name(): String = "int_identity"
+    override def produceResult(input: InternalRow): Int = input.getInt(0)
+  }
+
+  test("SPARK-58578: ApplyFunctionExpression is stateful and produces fresh copies") {
+    val expr = ApplyFunctionExpression(
+      intIdentity, Seq(BoundReference(0, IntegerType, nullable = false)))
+    assert(expr.stateful, "ApplyFunctionExpression.stateful should be true")
+    val copy = expr.freshCopyIfContainsStatefulExpression()
+    assert(copy ne expr,
+      "freshCopyIfContainsStatefulExpression should return a new instance " +
+        "for ApplyFunctionExpression")
+    assert(copy.eval(InternalRow(7)) === 7)
+  }
+
+  test("SPARK-58578: fresh copies do not share the reused input row") {
+    val firstEvaluationStarted = new CountDownLatch(1)
+    val secondEvaluationStarted = new CountDownLatch(1)
+    val blockingIdentity = new ScalarFunction[Int] {
+      override def inputTypes(): Array[DataType] = Array(IntegerType)
+      override def resultType(): DataType = IntegerType
+      override def name(): String = "blocking_identity"
+      override def produceResult(input: InternalRow): Int = {
+        if (input.getInt(0) == 1) {
+          firstEvaluationStarted.countDown()
+          assert(secondEvaluationStarted.await(10, TimeUnit.SECONDS))
+        } else {
+          secondEvaluationStarted.countDown()
+        }
+        input.getInt(0)
+      }
+    }
+
+    val expr = ApplyFunctionExpression(
+      blockingIdentity, Seq(BoundReference(0, IntegerType, nullable = false)))
+    val firstEvaluator = expr.freshCopyIfContainsStatefulExpression()
+    val secondEvaluator = expr.freshCopyIfContainsStatefulExpression()
+
+    val executor = ThreadUtils.newDaemonFixedThreadPool(2, "apply-function-expression-test")
+    val executionContext = ExecutionContext.fromExecutorService(executor)
+    try {
+      val firstResult = Future(firstEvaluator.eval(InternalRow(1)))(executionContext)
+      assert(firstEvaluationStarted.await(10, TimeUnit.SECONDS))
+      val secondResult = Future(secondEvaluator.eval(InternalRow(2)))(executionContext)
+
+      assert(ThreadUtils.awaitResult(firstResult, 10.seconds) === 1)
+      assert(ThreadUtils.awaitResult(secondResult, 10.seconds) === 2)
+    } finally {
+      executor.shutdownNow()
+    }
+  }
+}