diff --git a/sqlmesh/core/engine_adapter/base.py b/sqlmesh/core/engine_adapter/base.py
index bd435db76f..fd3d9a5c5c 100644
--- a/sqlmesh/core/engine_adapter/base.py
+++ b/sqlmesh/core/engine_adapter/base.py
@@ -833,7 +833,9 @@ def _create_table_from_columns(
             and self.COMMENT_CREATION_TABLE.is_comment_command_only
             and self.comments_enabled
         ):
-            self._create_column_comments(table_name, column_descriptions)
+            self._create_column_comments(
+                table_name, column_descriptions, table_format=kwargs.get("table_format")
+            )
 
     def _build_schema_exp(
         self,
@@ -990,7 +992,9 @@ def _create_table_from_source_queries(
         ):
             self._create_table_comment(table_name, table_description)
         if column_descriptions and schema is None and self.comments_enabled:
-            self._create_column_comments(table_name, column_descriptions)
+            self._create_column_comments(
+                table_name, column_descriptions, table_format=kwargs.get("table_format")
+            )
 
     def _create_table(
         self,
@@ -3058,7 +3062,18 @@ def _create_column_comments(
         column_comments: t.Dict[str, str],
         table_kind: str = "TABLE",
         materialized_view: bool = False,
+        table_format: t.Optional[str] = None,
     ) -> None:
+        """Registers column comments with a post-creation command.
+
+        Args:
+            table_name: The name of the table or view.
+            column_comments: Mapping between the column name and its comment.
+            table_kind: The kind of object being commented on, `TABLE` or `VIEW`.
+            materialized_view: Whether the view is materialized.
+            table_format: The table format of the table, if any. Engines that require
+                format-specific DDL to alter a table use it to derive `table_kind`.
+        """
         table = exp.to_table(table_name)
 
         for col, comment in column_comments.items():
diff --git a/sqlmesh/core/engine_adapter/bigquery.py b/sqlmesh/core/engine_adapter/bigquery.py
index d136445114..8139e799a7 100644
--- a/sqlmesh/core/engine_adapter/bigquery.py
+++ b/sqlmesh/core/engine_adapter/bigquery.py
@@ -818,6 +818,7 @@ def _create_column_comments(
         column_comments: t.Dict[str, str],
         table_kind: str = "TABLE",
         materialized_view: bool = False,
+        table_format: t.Optional[str] = None,
     ) -> None:
         if not (table_kind == "VIEW" and materialized_view):
             table = self._get_table(table_name)
diff --git a/sqlmesh/core/engine_adapter/mysql.py b/sqlmesh/core/engine_adapter/mysql.py
index 6918cdec49..a20ba2af26 100644
--- a/sqlmesh/core/engine_adapter/mysql.py
+++ b/sqlmesh/core/engine_adapter/mysql.py
@@ -131,6 +131,7 @@ def _create_column_comments(
         column_comments: t.Dict[str, str],
         table_kind: str = "TABLE",
         materialized_view: bool = False,
+        table_format: t.Optional[str] = None,
     ) -> None:
         table = exp.to_table(table_name)
         table_sql = table.sql(dialect=self.dialect, identify=True)
diff --git a/sqlmesh/core/engine_adapter/snowflake.py b/sqlmesh/core/engine_adapter/snowflake.py
index d589b5d15b..885e1e7c1f 100644
--- a/sqlmesh/core/engine_adapter/snowflake.py
+++ b/sqlmesh/core/engine_adapter/snowflake.py
@@ -632,13 +632,20 @@ def _create_column_comments(
         column_comments: t.Dict[str, str],
         table_kind: str = "TABLE",
         materialized_view: bool = False,
+        table_format: t.Optional[str] = None,
     ) -> None:
         """
         Reference: https://docs.snowflake.com/en/sql-reference/sql/alter-table-column#syntax
+        Reference: https://docs.snowflake.com/en/sql-reference/sql/alter-iceberg-table#syntax
         """
         if not column_comments:
             return
 
+        # Snowflake rejects `ALTER TABLE` for Iceberg tables, it requires
+        # `ALTER ICEBERG TABLE` instead
+        if table_format and table_kind == "TABLE":
+            table_kind = f"{table_format.upper()} TABLE"
+
         table = exp.to_table(table_name)
         table_sql = self._to_sql(table)
 
diff --git a/tests/core/engine_adapter/test_snowflake.py b/tests/core/engine_adapter/test_snowflake.py
index 085c51098b..1e772d8d29 100644
--- a/tests/core/engine_adapter/test_snowflake.py
+++ b/tests/core/engine_adapter/test_snowflake.py
@@ -246,6 +246,38 @@ def test_multiple_column_comments(make_mocked_engine_adapter: t.Callable, mocker
     ]
 
 
+def test_column_comments_iceberg(make_mocked_engine_adapter: t.Callable):
+    adapter = make_mocked_engine_adapter(SnowflakeEngineAdapter)
+
+    adapter._create_column_comments(
+        "test_table",
+        {"a": "a column description", "b": "b column description"},
+        table_format="iceberg",
+    )
+
+    assert to_sql_calls(adapter) == [
+        """ALTER ICEBERG TABLE "test_table" ALTER COLUMN "a" COMMENT 'a column description', COLUMN "b" COMMENT 'b column description'""",
+    ]
+
+
+def test_ctas_column_comments_iceberg(make_mocked_engine_adapter: t.Callable):
+    adapter = make_mocked_engine_adapter(SnowflakeEngineAdapter)
+
+    # The column types are unknown, so the comments can't be inlined into the CTAS
+    # schema definition and are registered with a post-creation ALTER instead
+    adapter.ctas(
+        "test_table",
+        parse_one("SELECT a, b FROM source_table"),
+        table_format="iceberg",
+        column_descriptions={"a": "a column description"},
+    )
+
+    assert to_sql_calls(adapter) == [
+        """CREATE ICEBERG TABLE IF NOT EXISTS "test_table" AS SELECT "a", "b" FROM "source_table\"""",
+        """ALTER ICEBERG TABLE "test_table" ALTER COLUMN "a" COMMENT 'a column description'""",
+    ]
+
+
 def test_sync_grants_config(make_mocked_engine_adapter: t.Callable, mocker: MockerFixture):
     adapter = make_mocked_engine_adapter(SnowflakeEngineAdapter)
     relation = normalize_identifiers(