diff --git a/Library/Homebrew/extend/os/linux/extend/ENV/shared.rb b/Library/Homebrew/extend/os/linux/extend/ENV/shared.rb
index 2d42c97b9c652..75ccb956fd408 100644
--- a/Library/Homebrew/extend/os/linux/extend/ENV/shared.rb
+++ b/Library/Homebrew/extend/os/linux/extend/ENV/shared.rb
@@ -7,8 +7,10 @@ def effective_arch
       @bottle_arch.to_sym
     elsif @build_bottle
       Hardware.oldest_cpu
-    else
+    elsif Hardware::CPU.intel? || Hardware::CPU.arm?
       :native
+    else
+      :none
     end
   end
 end
diff --git a/Library/Homebrew/hardware.rb b/Library/Homebrew/hardware.rb
index d970ced6f2379..138b5e118fe20 100644
--- a/Library/Homebrew/hardware.rb
+++ b/Library/Homebrew/hardware.rb
@@ -27,6 +27,7 @@ class << self
       sig { returns(T::Hash[Symbol, String]) }
       def optimization_flags
         @optimization_flags ||= T.let({
+          none:               "",
           native:             arch_flag("native"),
           ivybridge:          "-march=ivybridge",
           sandybridge:        "-march=sandybridge",