The Tramadol Nights star told The Guardian that he is not a fan of Lee, who is currently touring new show Carpet Remnant World.
Boyle said of Lee: "It seems to me [he's] irrelevant and flabby. Okay, you don't like Russell Howard; that's fine. But don't put on your posters 'a new kind of political comedy'.
"Yeah, without any politics. Crisps? What the f**k is that about? People internalise marketing. You sell yourself and people sell stuff to you.
"He ends up going, 'Michael McIntyre, Russell Howard, not like me'. What the f**k is that? Sick of that old washing powder?"
Talking to Digital Spy about Boyle's controversial material earlier this year, Lee said: "He writes good jokes, but they don't seem to have a consistent point of view.
"When some of the things he said are explained in certain terms, that point of view is then contradicted by another joke. It's hard to justify them, because they don't add up to a coherent world view."
Lee added: "I think the other problem Frankie has is that Channel 4 are defending him and we know that Channel 4 is run by opportunistic, moronic cynics."
Watch Stewart Lee talking about Frankie Boyle during a live show below:
> Frankie Boyle to host Channel 4 talkshow
> Frankie Boyle welcome back at Channel 4, says Jay Hunt
Watch an unseen sketch from Frankie Boyle's Tramadol Nights below: