diff --git a/changelog/fix_infinite_loop_on_style_multiline_ternary_operator.md b/changelog/fix_infinite_loop_on_style_multiline_ternary_operator.md
new file mode 100644
index 00000000000..beb0bccf347
--- /dev/null
+++ b/changelog/fix_infinite_loop_on_style_multiline_ternary_operator.md
@@ -0,0 +1 @@
+* [#10592](https://github.com/rubocop/rubocop/issues/10592): Fix infinite loop on `Style/MultilineTernaryOperator` if using assignment method and condition/branch is multiline. ([@nobuyo][])
diff --git a/lib/rubocop/cop/style/multiline_ternary_operator.rb b/lib/rubocop/cop/style/multiline_ternary_operator.rb
index 7d1bdbf57e6..20e993d7888 100644
--- a/lib/rubocop/cop/style/multiline_ternary_operator.rb
+++ b/lib/rubocop/cop/style/multiline_ternary_operator.rb
@@ -73,7 +73,11 @@ def replacement(node)
         end
 
         def enforce_single_line_ternary_operator?(node)
-          SINGLE_LINE_TYPES.include?(node.parent.type)
+          SINGLE_LINE_TYPES.include?(node.parent.type) && !use_assignment_method?(node.parent)
+        end
+
+        def use_assignment_method?(node)
+          node.send_type? && node.assignment_method?
         end
       end
     end
diff --git a/spec/rubocop/cop/style/multiline_ternary_operator_spec.rb b/spec/rubocop/cop/style/multiline_ternary_operator_spec.rb
index 30ad1edbef5..29059b00c0c 100644
--- a/spec/rubocop/cop/style/multiline_ternary_operator_spec.rb
+++ b/spec/rubocop/cop/style/multiline_ternary_operator_spec.rb
@@ -51,6 +51,63 @@
     RUBY
   end
 
+  it 'registers an offense and corrects when condition is multiline' do
+    expect_offense(<<~RUBY)
+      a =
+        b ==
+        ^^^^ Avoid multi-line ternary operators, use `if` or `unless` instead.
+          c ? d : e
+    RUBY
+
+    expect_correction(<<~RUBY)
+      a =
+        if b ==
+          c
+        d
+      else
+        e
+      end
+    RUBY
+  end
+
+  it 'registers an offense and corrects when condition is multiline and using hash key assignment' do
+    expect_offense(<<~RUBY)
+      a[:a] =
+        b ==
+        ^^^^ Avoid multi-line ternary operators, use `if` or `unless` instead.
+          c ? d : e
+    RUBY
+
+    expect_correction(<<~RUBY)
+      a[:a] =
+        if b ==
+          c
+        d
+      else
+        e
+      end
+    RUBY
+  end
+
+  it 'registers an offense and corrects when condition is multiline and using assignment method' do
+    expect_offense(<<~RUBY)
+      a.foo =
+        b ==
+        ^^^^ Avoid multi-line ternary operators, use `if` or `unless` instead.
+          c ? d : e
+    RUBY
+
+    expect_correction(<<~RUBY)
+      a.foo =
+        if b ==
+          c
+        d
+      else
+        e
+      end
+    RUBY
+  end
+
   it 'register an offense and corrects when returning a multiline ternary operator expression with `return`' do
     expect_offense(<<~RUBY)
       return cond ?