diff --git a/dev/tasks/linux-packages/apache-arrow/debian/control.in b/dev/tasks/linux-packages/apache-arrow/debian/control.in
index acb57c1fbc1..75481ec2985 100644
--- a/dev/tasks/linux-packages/apache-arrow/debian/control.in
+++ b/dev/tasks/linux-packages/apache-arrow/debian/control.in
@@ -56,6 +56,7 @@ Multi-Arch: same
 Pre-Depends: ${misc:Pre-Depends}
 Depends:
   ${misc:Depends},
+@USE_SYSTEM_OPEN_TELEMETRY@  opentelemetry-cpp,
   ${shlibs:Depends}
 Description: Apache Arrow is a data processing library for analysis
  .
diff --git a/dev/tasks/linux-packages/apache-arrow/test/test_debian_runtime_dependencies.rb b/dev/tasks/linux-packages/apache-arrow/test/test_debian_runtime_dependencies.rb
new file mode 100644
index 00000000000..541f9532cb5
--- /dev/null
+++ b/dev/tasks/linux-packages/apache-arrow/test/test_debian_runtime_dependencies.rb
@@ -0,0 +1,65 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+require "minitest/autorun"
+require "rake"
+
+package_dir = File.expand_path("..", __dir__)
+Dir.chdir(package_dir) do
+  load "Rakefile"
+end
+
+class DebianRuntimeDependenciesTest < Minitest::Test
+  def setup
+    @task = ApacheArrowPackageTask.new
+    @control_template = File.read(File.join(__dir__, "../debian/control.in"))
+    @libarrow_package = @control_template[/^Package: (libarrow\d+)$/, 1]
+    refute_nil(@libarrow_package, "missing libarrow package stanza")
+  end
+
+  def rendered_control(target)
+    @task.send(:apt_prepare_debian_control, @control_template, target)
+  end
+
+  def runtime_dependencies(control, package)
+    stanza = control.split(/^Package: /).find do |candidate|
+      candidate.start_with?("#{package}\n")
+    end
+    refute_nil(stanza, "missing package stanza for #{package}")
+    depends = stanza[/^Depends:\n((?:[ \t].*\n)+)/, 1]
+    refute_nil(depends, "missing Depends field for #{package}")
+    depends.lines.reject do |line|
+      line.lstrip.start_with?("#")
+    end.join
+  end
+
+  def test_system_open_telemetry_target_requires_its_runtime_package
+    %w[debian-trixie ubuntu-resolute].each do |target|
+      dependencies = runtime_dependencies(rendered_control(target),
+                                          @libarrow_package)
+      assert_match(/\bopentelemetry-cpp\b/, dependencies, target)
+    end
+  end
+
+  def test_target_without_system_open_telemetry_has_no_runtime_dependency
+    %w[ubuntu-jammy ubuntu-noble].each do |target|
+      dependencies = runtime_dependencies(rendered_control(target),
+                                          @libarrow_package)
+      refute_match(/\bopentelemetry-cpp\b/, dependencies, target)
+    end
+  end
+end