diff --git a/docs/v6_migration.rst b/docs/v6_migration.rst
index 74da70889e..97d80f7aba 100644
--- a/docs/v6_migration.rst
+++ b/docs/v6_migration.rst
@@ -76,6 +76,9 @@ Other Misc Changes
 
 - ``InfuraKeyNotFound`` exception has been changed to ``InfuraProjectIdNotFound``
 - ``SolidityError`` has been removed in favor of ``ContractLogicError``
+- When a method is unavailable from a node provider (i.e. a response error
+  code of -32601 is returned), a ``MethodUnavailable`` error is
+  now raised instead of ``ValueError``
 
 Removals
 ~~~~~~~~
diff --git a/newsfragments/2796.breaking.rst b/newsfragments/2796.breaking.rst
new file mode 100644
index 0000000000..3494b00189
--- /dev/null
+++ b/newsfragments/2796.breaking.rst
@@ -0,0 +1 @@
+When a method is not supported by a node provider, raise a MethodUnavailable error instead of the generic ValueError.
diff --git a/tests/core/manager/test_response_formatters.py b/tests/core/manager/test_response_formatters.py
index 4b372f2349..505a146386 100644
--- a/tests/core/manager/test_response_formatters.py
+++ b/tests/core/manager/test_response_formatters.py
@@ -13,6 +13,7 @@
     BadResponseFormat,
     BlockNotFound,
     ContractLogicError,
+    MethodUnavailable,
     TransactionNotFound,
 )
 
@@ -32,6 +33,17 @@
     "message": "You cannot query logs for more than 10000 blocks at once.",
     "method": "eth_getLogs",
 }
+METHOD_NOT_FOUND_RESP_FORMAT = {
+    "jsonrpc": "2.0",
+    "error": {
+        "code": -32601,
+        "message": "the method eth_getTransactionByHash does not exist/is not "
+        "available",
+    },
+}
+ETH_TESTER_METHOD_NOT_FOUND_RESP_FORMAT = {
+    "error": "the method eth_getTransactionByHash does not exist/is not available",
+}
 
 
 def raise_contract_logic_error(response):
@@ -105,6 +117,20 @@ def raise_contract_logic_error(response):
             raise_transaction_not_found,
             TransactionNotFound,
         ),
+        (
+            METHOD_NOT_FOUND_RESP_FORMAT,
+            (),
+            identity,
+            identity,
+            MethodUnavailable,
+        ),
+        (
+            ETH_TESTER_METHOD_NOT_FOUND_RESP_FORMAT,
+            (),
+            identity,
+            identity,
+            ValueError,
+        ),
     ],
 )
 def test_formatted_response_raises_errors(
diff --git a/web3/exceptions.py b/web3/exceptions.py
index 8bd5288f86..235b9ee8ea 100644
--- a/web3/exceptions.py
+++ b/web3/exceptions.py
@@ -287,3 +287,11 @@ class BadResponseFormat(Web3Exception):
     """
 
     pass
+
+
+class MethodUnavailable(Web3Exception):
+    """
+    Raised when the method is not available on the node
+    """
+
+    pass
diff --git a/web3/manager.py b/web3/manager.py
index ffab72d7d8..fed4c1c786 100644
--- a/web3/manager.py
+++ b/web3/manager.py
@@ -34,6 +34,7 @@
 )
 from web3.exceptions import (
     BadResponseFormat,
+    MethodUnavailable,
 )
 from web3.middleware import (
     abi_middleware,
@@ -188,6 +189,13 @@ def formatted_response(
     ) -> Any:
         if "error" in response:
             apply_error_formatters(error_formatters, response)
+
+            # guard against eth-tester case - eth-tester returns a string
+            # with no code, so can't parse what the error is.
+            if isinstance(response["error"], dict):
+                resp_code = response["error"].get("code")
+                if resp_code == -32601:
+                    raise MethodUnavailable(response["error"])
             raise ValueError(response["error"])
         # NULL_RESPONSES includes None, so return False here as the default
         # so we don't apply the null_result_formatters if there is no 'result' key