"The Nationals brand across regional Western Australia has suffered as a result of Mr Joyce's actions and he has become a distraction at both Federal and State level."
There are no Western Australian Nationals in federal parliament, but it has nine members in WA's Legislative Assembly and Legislative Council.
"It is the view of the [WA Nationals] that Mr Joyce's position as Federal Leader is no longer tenable," the statement said.
Nationals MPs have spent the last week publicly speculating about Mr Joyce's future, with the party believed to be split in its support for him.
The Resources Minister, Matt Canavan, played down the statement from the WA leader Mia Davies.
"She's of course entitled to her opinion and it's one I can understand but I think the interest of the National Party and regional Australia is still served by Barnaby staying there to fight for regional areas," Mr Canavan told reporters at Parliament House.
"There's a level of disappointment about what's happened but they don't want to see a change of direction because there's a level of trepidation about the leadership for regional Australia that would be replaced if Barnaby's no longer leading the National Party."
Mr Joyce is taking a week of personal leave while Prime Minister Malcolm Turnbull travels to Washington to meet with the US President.
It means Mr Joyce is not filling the symbolic position of Deputy Prime Minister, which is instead being filled by the Finance Minister Mathias Cormann.