diff --git a/arrow/src/compute/kernels/aggregate.rs b/arrow/src/compute/kernels/aggregate.rs
index c8d0443c470..fb2f55582d6 100644
--- a/arrow/src/compute/kernels/aggregate.rs
+++ b/arrow/src/compute/kernels/aggregate.rs
@@ -185,7 +185,7 @@ pub fn min_string<T: OffsetSizeTrait>(array: &GenericStringArray<T>) -> Option<&
 }
 
 /// Returns the sum of values in the array.
-pub fn sum_dyn<T, A: ArrayAccessor<Item = T::Native>>(array: A) -> Option<T::Native>
+pub fn sum_array<T, A: ArrayAccessor<Item = T::Native>>(array: A) -> Option<T::Native>
 where
     T: ArrowNumericType,
     T::Native: Add<Output = T::Native>,
@@ -215,6 +215,68 @@ where
     }
 }
 
+/// Returns the min of values in the array.
+pub fn min_array<T, A: ArrayAccessor<Item = T::Native>>(array: A) -> Option<T::Native>
+where
+    T: ArrowNumericType,
+    T::Native: ArrowNativeType,
+{
+    min_max_array_helper::<T, A, _, _>(
+        array,
+        |a, b| (!is_nan(*a) & is_nan(*b)) || a < b,
+        min,
+    )
+}
+
+/// Returns the max of values in the array.
+pub fn max_array<T, A: ArrayAccessor<Item = T::Native>>(array: A) -> Option<T::Native>
+where
+    T: ArrowNumericType,
+    T::Native: ArrowNativeType,
+{
+    min_max_array_helper::<T, A, _, _>(
+        array,
+        |a, b| (is_nan(*a) & !is_nan(*b)) || a > b,
+        max,
+    )
+}
+
+fn min_max_array_helper<T, A: ArrayAccessor<Item = T::Native>, F, M>(
+    array: A,
+    cmp: F,
+    m: M,
+) -> Option<T::Native>
+where
+    T: ArrowNumericType,
+    F: Fn(&T::Native, &T::Native) -> bool,
+    M: Fn(&PrimitiveArray<T>) -> Option<T::Native>,
+{
+    match array.data_type() {
+        DataType::Dictionary(_, _) => {
+            let null_count = array.null_count();
+
+            if null_count == array.len() {
+                return None;
+            }
+
+            let mut has_value = false;
+            let mut n = T::default_value();
+            let iter = ArrayIter::new(array);
+            iter.into_iter().for_each(|value| {
+                if let Some(value) = value {
+                    if !has_value || cmp(&value, &n) {
+                        has_value = true;
+                        n = value;
+                    }
+                }
+            });
+
+            Some(n)
+        }
+        _ => m(as_primitive_array(&array)),
+    }
+}
+
 /// Returns the sum of values in the primitive array.
 ///
 /// Returns `None` if the array is empty or only contains null values.
@@ -656,7 +718,7 @@ mod tests {
     use super::*;
     use crate::array::*;
     use crate::compute::add;
-    use crate::datatypes::{Int32Type, Int8Type};
+    use crate::datatypes::{Float32Type, Int32Type, Int8Type};
 
     #[test]
     fn test_primitive_array_sum() {
@@ -1043,19 +1105,63 @@ mod tests {
 
         let dict_array = DictionaryArray::try_new(&keys, &values).unwrap();
         let array = dict_array.downcast_dict::<Int8Array>().unwrap();
-        assert_eq!(39, sum_dyn::<Int8Type, _>(array).unwrap());
+        assert_eq!(39, sum_array::<Int8Type, _>(array).unwrap());
 
         let a = Int32Array::from(vec![1, 2, 3, 4, 5]);
-        assert_eq!(15, sum_dyn::<Int32Type, _>(&a).unwrap());
+        assert_eq!(15, sum_array::<Int32Type, _>(&a).unwrap());
 
         let keys = Int8Array::from(vec![Some(2_i8), None, Some(4)]);
         let dict_array = DictionaryArray::try_new(&keys, &values).unwrap();
         let array = dict_array.downcast_dict::<Int8Array>().unwrap();
-        assert_eq!(26, sum_dyn::<Int8Type, _>(array).unwrap());
+        assert_eq!(26, sum_array::<Int8Type, _>(array).unwrap());
+
+        let keys = Int8Array::from(vec![None, None, None]);
+        let dict_array = DictionaryArray::try_new(&keys, &values).unwrap();
+        let array = dict_array.downcast_dict::<Int8Array>().unwrap();
+        assert!(sum_array::<Int8Type, _>(array).is_none());
+    }
+
+    #[test]
+    fn test_max_min_dyn() {
+        let values = Int8Array::from_iter_values([10_i8, 11, 12, 13, 14, 15, 16, 17]);
+        let keys = Int8Array::from_iter_values([2_i8, 3, 4]);
+
+        let dict_array = DictionaryArray::try_new(&keys, &values).unwrap();
+        let array = dict_array.downcast_dict::<Int8Array>().unwrap();
+        assert_eq!(14, max_array::<Int8Type, _>(array).unwrap());
+
+        let array = dict_array.downcast_dict::<Int8Array>().unwrap();
+        assert_eq!(12, min_array::<Int8Type, _>(array).unwrap());
+
+        let a = Int32Array::from(vec![1, 2, 3, 4, 5]);
+        assert_eq!(5, max_array::<Int32Type, _>(&a).unwrap());
+        assert_eq!(1, min_array::<Int32Type, _>(&a).unwrap());
+
+        let keys = Int8Array::from(vec![Some(2_i8), None, Some(7)]);
+        let dict_array = DictionaryArray::try_new(&keys, &values).unwrap();
+        let array = dict_array.downcast_dict::<Int8Array>().unwrap();
+        assert_eq!(17, max_array::<Int8Type, _>(array).unwrap());
+        let array = dict_array.downcast_dict::<Int8Array>().unwrap();
+        assert_eq!(12, min_array::<Int8Type, _>(array).unwrap());
 
         let keys = Int8Array::from(vec![None, None, None]);
         let dict_array = DictionaryArray::try_new(&keys, &values).unwrap();
         let array = dict_array.downcast_dict::<Int8Array>().unwrap();
-        assert!(sum_dyn::<Int8Type, _>(array).is_none());
+        assert!(max_array::<Int8Type, _>(array).is_none());
+        let array = dict_array.downcast_dict::<Int8Array>().unwrap();
+        assert!(min_array::<Int8Type, _>(array).is_none());
+    }
+
+    #[test]
+    fn test_max_min_dyn_nan() {
+        let values = Float32Array::from(vec![5.0_f32, 2.0_f32, f32::NAN]);
+        let keys = Int8Array::from_iter_values([0_i8, 1, 2]);
+
+        let dict_array = DictionaryArray::try_new(&keys, &values).unwrap();
+        let array = dict_array.downcast_dict::<Float32Array>().unwrap();
+        assert!(max_array::<Float32Type, _>(array).unwrap().is_nan());
+
+        let array = dict_array.downcast_dict::<Float32Array>().unwrap();
+        assert_eq!(2.0_f32, min_array::<Float32Type, _>(array).unwrap());
     }
 }