No, "Go wash the dishes" isn't commonly used as sexist insult in (American) English. I don't really think of dish-washing as stereotypically related to women anyway, but that might differ for other people, I suppose.
That said, if you said it to a woman who was trying to give you advice on how to fix your car, the meaning would be taken.
There are two other phrases that come to mind, namely "Make me a sandwich" and "Get back in the kitchen." I think either one would be a suitable translation, although I would say the first is ruder (they are both very rude), since you are demanding the woman to do something for you, rather than just leaving the area/conversation.
Make me a sandwich
This one is mostly an Internet meme, see Know your Meme and the xckd comic linked in the comments:
(The joke here is that
sudo is a *nix administrator command that is used to force the computer to do something potentially dangerous. See Explain xkcd.)
The other phrase, closely tied to "make me a sandwich" is:
Get back in the kitchen
Again, from Know your Meme:
“Get Back In The Kitchen”, otherwise known as “Get Back To The Kitchen”, is a phrase often used in jest, typically as a hyperbolic response to an action performed by a woman that is more masculine than expected or that is independent. It is often followed by the phrase, “And make me a sandwich.” Additionally, it is also used regularly to make fun of people who actually believe that women should stay in the kitchen, depicting them as ignorant.
Although I would say this one is slightly less tied to the Internet in general.