diff --git a/sentry_sdk/integrations/opentelemetry/propagator.py b/sentry_sdk/integrations/opentelemetry/propagator.py
index a40f038ffa..5b5f13861d 100644
--- a/sentry_sdk/integrations/opentelemetry/propagator.py
+++ b/sentry_sdk/integrations/opentelemetry/propagator.py
@@ -109,7 +109,7 @@ def inject(
 
         span_id = trace.format_span_id(current_span_context.span_id)
 
-        span_map = SentrySpanProcessor().otel_span_map
+        span_map = SentrySpanProcessor.otel_span_map
         sentry_span = span_map.get(span_id, None)
         if not sentry_span:
             return
diff --git a/sentry_sdk/integrations/opentelemetry/span_processor.py b/sentry_sdk/integrations/opentelemetry/span_processor.py
index 8a589af308..de7d10a762 100644
--- a/sentry_sdk/integrations/opentelemetry/span_processor.py
+++ b/sentry_sdk/integrations/opentelemetry/span_processor.py
@@ -83,6 +83,8 @@ class SentrySpanProcessor(SpanProcessor):
     # The currently open spans. Elements will be discarded after SPAN_MAX_TIME_OPEN_MINUTES
     open_spans: "dict[int, set[str]]" = {}
 
+    initialized: "bool" = False
+
     def __new__(cls) -> "SentrySpanProcessor":
         if not hasattr(cls, "instance"):
             cls.instance = super().__new__(cls)
@@ -91,10 +93,15 @@ def __new__(cls) -> "SentrySpanProcessor":
         return cls.instance  # type: ignore[misc]
 
     def __init__(self) -> None:
+        if self.initialized:
+            return
+
         @add_global_event_processor
         def global_event_processor(event: "Event", hint: "Hint") -> "Event":
             return link_trace_context_to_error_event(event, self.otel_span_map)
 
+        self.initialized = True
+
     def _prune_old_spans(self: "SentrySpanProcessor") -> None:
         """
         Prune spans that have been open for too long.
diff --git a/tests/integrations/opentelemetry/test_propagator.py b/tests/integrations/opentelemetry/test_propagator.py
index d999b0bb2b..4374098b23 100644
--- a/tests/integrations/opentelemetry/test_propagator.py
+++ b/tests/integrations/opentelemetry/test_propagator.py
@@ -1,3 +1,10 @@
+from sentry_sdk.integrations.opentelemetry.integration import (
+    OpenTelemetryIntegration,
+)
+from opentelemetry import trace
+from sentry_sdk.scope import global_event_processors
+
+
 import pytest
 
 from unittest import mock
@@ -298,3 +305,21 @@ def test_inject_sentry_span_baggage():
             "baggage",
             baggage.serialize(),
         )
+
+
+def test_inject_no_memory_leak():
+
+    OpenTelemetryIntegration.setup_once()
+
+    tracer = trace.get_tracer(__name__)
+    propagator = SentryPropagator()
+
+    cnt_before = len(global_event_processors)
+
+    with tracer.start_as_current_span("bar") as new_span:
+        context = set_span_in_context(new_span)
+        carrier = "any_carrier"
+        propagator.inject(carrier, context)
+
+    cnt_after = len(global_event_processors)
+    assert cnt_after == cnt_before
diff --git a/tests/integrations/opentelemetry/test_span_processor.py b/tests/integrations/opentelemetry/test_span_processor.py
index e1cd849b94..0444475ffa 100644
--- a/tests/integrations/opentelemetry/test_span_processor.py
+++ b/tests/integrations/opentelemetry/test_span_processor.py
@@ -1,3 +1,4 @@
+from sentry_sdk.scope import global_event_processors
 import time
 from datetime import datetime, timezone
 from unittest import mock
@@ -621,3 +622,14 @@ def test_pruning_old_spans_on_end():
     span_processor.on_end(otel_span)
     assert sorted(list(span_processor.otel_span_map.keys())) == ["111111111abcdef"]
     assert sorted(list(span_processor.open_spans.values())) == [{"111111111abcdef"}]
+
+
+def test_no_memory_leak():
+    span_processor_1 = SentrySpanProcessor()
+    cnt_before = len(global_event_processors)
+
+    span_processor_2 = SentrySpanProcessor()
+
+    cnt_after = len(global_event_processors)
+    assert span_processor_1 is span_processor_2
+    assert cnt_before == cnt_after