diff --git a/haystack/components/generators/chat/fallback.py b/haystack/components/generators/chat/fallback.py
index 091c4aa5ab9..01968f5d8be 100644
--- a/haystack/components/generators/chat/fallback.py
+++ b/haystack/components/generators/chat/fallback.py
@@ -60,6 +60,7 @@ def __init__(self, chat_generators: list[ChatGenerator]) -> None:
             raise ValueError(msg)
 
         self.chat_generators = list(chat_generators)
+        self._warmed_up = False
 
     def to_dict(self) -> dict[str, Any]:
         """Serialize the component, including nested chat generators."""
@@ -87,18 +88,22 @@ def from_dict(cls, data: dict[str, Any]) -> FallbackChatGenerator:
         return default_from_dict(cls, data)
 
     def warm_up(self) -> None:
-        """Warm up all underlying chat generators."""
-        for gen in self.chat_generators:
-            if hasattr(gen, "warm_up"):
-                gen.warm_up()
+        """Warm up all underlying chat generators (called at most once)."""
+        if not self._warmed_up:
+            for gen in self.chat_generators:
+                if hasattr(gen, "warm_up"):
+                    gen.warm_up()
+            self._warmed_up = True
 
     async def warm_up_async(self) -> None:
-        """Warm up all underlying chat generators on the serving event loop."""
-        for gen in self.chat_generators:
-            if hasattr(gen, "warm_up_async"):
-                await gen.warm_up_async()
-            elif hasattr(gen, "warm_up"):
-                gen.warm_up()
+        """Warm up all underlying chat generators on the serving event loop (called at most once)."""
+        if not self._warmed_up:
+            for gen in self.chat_generators:
+                if hasattr(gen, "warm_up_async"):
+                    await gen.warm_up_async()
+                elif hasattr(gen, "warm_up"):
+                    gen.warm_up()
+            self._warmed_up = True
 
     def close(self) -> None:
         """Release the underlying chat generators' resources."""
diff --git a/releasenotes/notes/fix-fallback-warm-up-lifecycle-da9d4b4af6a25872.yaml b/releasenotes/notes/fix-fallback-warm-up-lifecycle-da9d4b4af6a25872.yaml
new file mode 100644
index 00000000000..60929ac81a9
--- /dev/null
+++ b/releasenotes/notes/fix-fallback-warm-up-lifecycle-da9d4b4af6a25872.yaml
@@ -0,0 +1,9 @@
+---
+fixes:
+  - |
+    ``FallbackChatGenerator`` now follows the same ``warm_up`` lifecycle semantics as
+    every other Haystack component. Previously, ``warm_up()`` was called on every
+    ``run()`` and ``run_async()`` invocation, meaning wrapped generators could be
+    initialized multiple times. This is now guarded by a ``_warmed_up`` flag so that
+    each underlying generator is warmed up at most once, regardless of how many times
+    the component is invoked.
diff --git a/test/components/generators/chat/test_fallback.py b/test/components/generators/chat/test_fallback.py
index c654e209221..e12897bd2b3 100644
--- a/test/components/generators/chat/test_fallback.py
+++ b/test/components/generators/chat/test_fallback.py
@@ -385,6 +385,19 @@ def test_warm_up_delegates_to_every_generator(self):
         for gen in gens:
             gen.warm_up.assert_called_once()
 
+    def test_warm_up_only_called_once_across_multiple_run_calls(self):
+        """warm_up() must not be re-invoked on every run(); generators are initialized at most once."""
+        gens = [Mock(spec=["run", "warm_up"]) for _ in range(2)]
+        for gen in gens:
+            gen.run.return_value = {"replies": [ChatMessage.from_assistant("ok")], "meta": {}}
+        fallback = FallbackChatGenerator(chat_generators=gens)
+        # Call run() three times
+        for _ in range(3):
+            fallback.run([ChatMessage.from_user("hi")])
+        # warm_up must have been called exactly once despite three run() calls
+        for gen in gens:
+            gen.warm_up.assert_called_once()
+
     async def test_warm_up_async_delegates_to_every_generator(self):
         gens = [Mock(spec=["run", "warm_up_async"]) for _ in range(3)]
         for gen in gens:
@@ -394,6 +407,18 @@ async def test_warm_up_async_delegates_to_every_generator(self):
         for gen in gens:
             gen.warm_up_async.assert_awaited_once()
 
+    async def test_warm_up_async_only_called_once_across_multiple_run_async_calls(self):
+        """warm_up_async() must not be re-invoked on every run_async(); generators are initialized at most once."""
+        gens = [Mock(spec=["run_async", "warm_up_async"]) for _ in range(2)]
+        for gen in gens:
+            gen.warm_up_async = AsyncMock()
+            gen.run_async = AsyncMock(return_value={"replies": [ChatMessage.from_assistant("ok")], "meta": {}})
+        fallback = FallbackChatGenerator(chat_generators=gens)
+        for _ in range(3):
+            await fallback.run_async([ChatMessage.from_user("hi")])
+        for gen in gens:
+            gen.warm_up_async.assert_awaited_once()
+
     async def test_warm_up_async_falls_back_to_sync_warm_up(self):
         gens = [Mock(spec=["run", "warm_up"]) for _ in range(3)]
         fallback = FallbackChatGenerator(chat_generators=gens)