diff --git a/CHANGELOG.md b/CHANGELOG.md
index facf7914145..33b21cabce7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,7 @@
 ### Bug fixes
 
 * [#8115](https://github.com/rubocop-hq/rubocop/issues/8115): Fix false negative for `Lint::FormatParameterMismatch` when argument contains formatting. ([@andrykonchin][])
+* [#8131](https://github.com/rubocop-hq/rubocop/pull/8131): Fix false positive for Style/RedundantRegexpEscape with escaped delimiters. ([@owst][])
 * [#8124](https://github.com/rubocop-hq/rubocop/issues/8124): Fix a false positive for `Lint/FormatParameterMismatch` when using named parameters with escaped `%`. ([@koic][])
 
 ## 0.85.1 (2020-06-07)
diff --git a/docs/modules/ROOT/pages/cops_style.adoc b/docs/modules/ROOT/pages/cops_style.adoc
index aefaa80e5b1..96c268e7ba5 100644
--- a/docs/modules/ROOT/pages/cops_style.adoc
+++ b/docs/modules/ROOT/pages/cops_style.adoc
@@ -7180,6 +7180,9 @@ This cop checks for redundant escapes inside Regexp literals.
 # good
 %r/foo\/bar/
 
+# good
+%r!foo\!bar!
+
 # bad
 /a\-b/
 
diff --git a/lib/rubocop/cop/style/redundant_regexp_escape.rb b/lib/rubocop/cop/style/redundant_regexp_escape.rb
index 426491e6f0a..8ee6ade144f 100644
--- a/lib/rubocop/cop/style/redundant_regexp_escape.rb
+++ b/lib/rubocop/cop/style/redundant_regexp_escape.rb
@@ -18,6 +18,9 @@ module Style
       #   # good
       #   %r/foo\/bar/
       #
+      #   # good
+      #   %r!foo\!bar!
+      #
       #   # bad
       #   /a\-b/
       #
@@ -63,27 +66,30 @@ def autocorrect(node)
 
         private
 
-        def slash_literal?(node)
-          ['/', '%r/'].include?(node.loc.begin.source)
-        end
-
         def allowed_escape?(node, char, within_character_class)
           # Strictly speaking a few single-letter metachars are currently
           # unnecessary to "escape", e.g. g, i, E, F, but enumerating them is
           # rather difficult, and their behaviour could change over time with
           # different versions of Ruby so that e.g. /\g/ != /g/
           return true if /[[:alnum:]]/.match?(char)
-          return true if ALLOWED_ALWAYS_ESCAPES.include?(char)
+          return true if ALLOWED_ALWAYS_ESCAPES.include?(char) || delimiter?(node, char)
 
-          if char == '/'
-            slash_literal?(node)
-          elsif within_character_class
+          if within_character_class
             ALLOWED_WITHIN_CHAR_CLASS_METACHAR_ESCAPES.include?(char)
           else
             ALLOWED_OUTSIDE_CHAR_CLASS_METACHAR_ESCAPES.include?(char)
           end
         end
 
+        def delimiter?(node, char)
+          delimiters = [
+            node.loc.begin.source.chars.last,
+            node.loc.end.source.chars.first
+          ]
+
+          delimiters.include?(char)
+        end
+
         def each_escape(node)
           pattern_source(node).each_char.with_index.reduce(
             [nil, false]
diff --git a/spec/rubocop/cop/style/redundant_regexp_escape_spec.rb b/spec/rubocop/cop/style/redundant_regexp_escape_spec.rb
index 64fa3abe69b..835ac863539 100644
--- a/spec/rubocop/cop/style/redundant_regexp_escape_spec.rb
+++ b/spec/rubocop/cop/style/redundant_regexp_escape_spec.rb
@@ -249,6 +249,18 @@
       end
     end
 
+    context 'with an escaped { or } outside a character class' do
+      it 'does not register an offense' do
+        expect_no_offenses('foo = %r{\{\}}')
+      end
+    end
+
+    context 'with an escaped { or } inside a character class' do
+      it 'does not register an offense' do
+        expect_no_offenses('foo = %r{[\{\}]}')
+      end
+    end
+
     context 'with redundantly-escaped slashes' do
       it 'registers an offense and corrects' do
         expect_offense(<<~'RUBY')
@@ -264,6 +276,46 @@
     end
   end
 
+  [
+    '!',
+    '~',
+    '@',
+    '_',
+    '^',
+    '<>',
+    '()'
+  ].each do |delims|
+    l, r = delims.chars
+    r = l if r.nil?
+    escaped_delims = "\\#{l}\\#{r}"
+
+    context "with a single-line %r#{l}#{r} regexp" do
+      context 'without escapes' do
+        it 'does not register an offense' do
+          expect_no_offenses("foo = %r#{l}a#{r}")
+        end
+      end
+
+      context 'with escaped delimiters and regexp options' do
+        it 'does not register an offense' do
+          expect_no_offenses("foo = %r#{l}#{escaped_delims}#{r}i")
+        end
+      end
+
+      context 'with escaped delimiters outside a character-class' do
+        it 'does not register an offense' do
+          expect_no_offenses("foo = %r#{l}#{escaped_delims}#{r}")
+        end
+      end
+
+      context 'with escaped delimiters inside a character-class' do
+        it 'does not register an offense' do
+          expect_no_offenses("foo = %r#{l}a[#{escaped_delims}]b#{r}")
+        end
+      end
+    end
+  end
+
   context 'with a single-line %r// regexp' do
     context 'without escapes' do
       it 'does not register an offense' do