diff --git a/src/cfnlint/data/schemas/extensions/aws_ec2_instance/privateipaddress.json b/src/cfnlint/data/schemas/extensions/aws_ec2_instance/privateipaddress.json
new file mode 100644
index 0000000000..c115d4a5a4
--- /dev/null
+++ b/src/cfnlint/data/schemas/extensions/aws_ec2_instance/privateipaddress.json
@@ -0,0 +1,30 @@
+{
+ "if": {
+  "required": [
+   "PrivateIpAddress"
+  ]
+ },
+ "then": {
+  "properties": {
+   "NetworkInterfaces": {
+    "items": {
+     "properties": {
+      "PrivateIpAddresses": {
+       "items": {
+        "properties": {
+         "Primary": {
+          "enum": [
+           false
+          ]
+         }
+        }
+       },
+       "type": "array"
+      }
+     }
+    },
+    "type": "array"
+   }
+  }
+ }
+}
diff --git a/src/cfnlint/rules/resources/ectwo/PrivateIpWithNetworkInterface.py b/src/cfnlint/rules/resources/ectwo/PrivateIpWithNetworkInterface.py
new file mode 100644
index 0000000000..47cbc92a4c
--- /dev/null
+++ b/src/cfnlint/rules/resources/ectwo/PrivateIpWithNetworkInterface.py
@@ -0,0 +1,33 @@
+"""
+Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+SPDX-License-Identifier: MIT-0
+"""
+
+from __future__ import annotations
+
+from typing import Any
+
+import cfnlint.data.schemas.extensions.aws_ec2_instance
+from cfnlint.jsonschema import ValidationError
+from cfnlint.rules.jsonschema.CfnLintJsonSchema import CfnLintJsonSchema, SchemaDetails
+
+
+class PrivateIpWithNetworkInterface(CfnLintJsonSchema):
+    id = "E3674"
+    shortdesc = "Primary cannoy be True when PrivateIpAddress is specified"
+    description = "Only specify the private IP address for an instance in one spot"
+    tags = ["resources", "ec2"]
+
+    def __init__(self) -> None:
+        super().__init__(
+            keywords=[
+                "Resources/AWS::EC2::Instance/Properties",
+            ],
+            schema_details=SchemaDetails(
+                module=cfnlint.data.schemas.extensions.aws_ec2_instance,
+                filename="privateipaddress.json",
+            ),
+        )
+
+    def message(self, instance: Any, err: ValidationError) -> str:
+        return "'Primary' cannot be True when 'PrivateIpAddress' is specified"
diff --git a/test/unit/rules/resources/ec2/test_private_ip_with_network_interafce.py b/test/unit/rules/resources/ec2/test_private_ip_with_network_interafce.py
new file mode 100644
index 0000000000..33acf75056
--- /dev/null
+++ b/test/unit/rules/resources/ec2/test_private_ip_with_network_interafce.py
@@ -0,0 +1,119 @@
+"""
+Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+SPDX-License-Identifier: MIT-0
+"""
+
+from collections import deque
+
+import pytest
+
+from cfnlint.jsonschema import ValidationError
+from cfnlint.rules.resources.ectwo.PrivateIpWithNetworkInterface import (
+    PrivateIpWithNetworkInterface,
+)
+
+
+@pytest.fixture(scope="module")
+def rule():
+    rule = PrivateIpWithNetworkInterface()
+    yield rule
+
+
+@pytest.mark.parametrize(
+    "name,instance,path,expected",
+    [
+        (
+            "Valid with no Private Ip Address",
+            {
+                "NetworkInterfaces": [
+                    {
+                        "PrivateIpAddresses": [
+                            {"PrivateIpAddress": "172.31.35.42", "Primary": True}
+                        ]
+                    }
+                ]
+            },
+            {
+                "path": ["Resources", "Instance", "Properties"],
+            },
+            [],
+        ),
+        (
+            "Valid with Private Ip Address with Primary False",
+            {
+                "PrivateIpAddress": "172.31.35.42",
+                "NetworkInterfaces": [
+                    {
+                        "PrivateIpAddresses": [
+                            {"PrivateIpAddress": "172.31.35.42", "Primary": False}
+                        ]
+                    }
+                ],
+            },
+            {
+                "path": ["Resources", "Instance", "Properties"],
+            },
+            [],
+        ),
+        (
+            "Valid with Private Ip Address without Primary specified",
+            {
+                "PrivateIpAddress": "172.31.35.42",
+                "NetworkInterfaces": [
+                    {"PrivateIpAddresses": [{"PrivateIpAddress": "172.31.35.42"}]}
+                ],
+            },
+            {
+                "path": ["Resources", "Instance", "Properties"],
+            },
+            [],
+        ),
+        (
+            "Invalid with a private ip address",
+            {
+                "PrivateIpAddress": "172.31.35.42",
+                "NetworkInterfaces": [
+                    {
+                        "PrivateIpAddresses": [
+                            {"PrivateIpAddress": "172.31.35.42", "Primary": True}
+                        ]
+                    }
+                ],
+            },
+            {
+                "path": ["Resources", "Instance", "Properties"],
+            },
+            [
+                ValidationError(
+                    "'Primary' cannot be True when 'PrivateIpAddress' is specified",
+                    validator="enum",
+                    rule=PrivateIpWithNetworkInterface(),
+                    path=deque(
+                        ["NetworkInterfaces", 0, "PrivateIpAddresses", 0, "Primary"]
+                    ),
+                    schema_path=deque(
+                        [
+                            "then",
+                            "properties",
+                            "NetworkInterfaces",
+                            "items",
+                            "properties",
+                            "PrivateIpAddresses",
+                            "items",
+                            "properties",
+                            "Primary",
+                            "enum",
+                        ]
+                    ),
+                )
+            ],
+        ),
+    ],
+    indirect=["path"],
+)
+def test_validate(name, instance, expected, rule, validator):
+    errs = list(rule.validate(validator, "", instance, {}))
+
+    assert (
+        errs == expected
+    ), f"Expected test {name!r} to have {expected!r} but got {errs!r}"