diff --git a/changelog/fix_false_positive_style_redundant_string_escape.md b/changelog/fix_false_positive_style_redundant_string_escape.md
new file mode 100644
index 00000000000..92232f93504
--- /dev/null
+++ b/changelog/fix_false_positive_style_redundant_string_escape.md
@@ -0,0 +1 @@
+* [#11346](https://github.com/rubocop/rubocop/issues/11346): Fix a false positive for `Style/RedundantStringEscape` when using escaped space in heredoc. ([@koic][])
diff --git a/lib/rubocop/cop/style/redundant_string_escape.rb b/lib/rubocop/cop/style/redundant_string_escape.rb
index 4eedd1c815c..291c9cd14be 100644
--- a/lib/rubocop/cop/style/redundant_string_escape.rb
+++ b/lib/rubocop/cop/style/redundant_string_escape.rb
@@ -76,6 +76,7 @@ def begin_loc_present?(node)
           node.loc.to_hash.key?(:begin) && !node.loc.begin.nil?
         end
 
+        # rubocop:disable Metrics/CyclomaticComplexity
         def allowed_escape?(node, range)
           escaped = range.source[(1..-1)]
 
@@ -88,13 +89,14 @@ def allowed_escape?(node, range)
           # with different versions of Ruby so that e.g. /\d/ != /d/
           return true if /[\n\\[[:alnum:]]]/.match?(escaped[0])
 
-          return true if escaped[0] == ' ' && percent_array_literal?(node)
+          return true if escaped[0] == ' ' && (percent_array_literal?(node) || node.heredoc?)
 
           return true if disabling_interpolation?(range)
           return true if delimiter?(node, escaped[0])
 
           false
         end
+        # rubocop:enable Metrics/CyclomaticComplexity
 
         def interpolation_not_enabled?(node)
           single_quoted?(node) ||
diff --git a/spec/rubocop/cop/style/redundant_string_escape_spec.rb b/spec/rubocop/cop/style/redundant_string_escape_spec.rb
index 0335b4d9cbf..a31fdce4f1f 100644
--- a/spec/rubocop/cop/style/redundant_string_escape_spec.rb
+++ b/spec/rubocop/cop/style/redundant_string_escape_spec.rb
@@ -417,6 +417,14 @@ def wrap(contents)
         MYHEREDOC
       RUBY
     end
+
+    it 'does register an offense an escaped space' do
+      expect_no_offenses(<<~'RUBY')
+        <<~MYHEREDOC
+          \ text
+        MYHEREDOC
+      RUBY
+    end
   end
 
   context 'with an interpolation-disabled HEREDOC' do