Mr Hunt said the First Minister's office would no longer routinely get help from Foreign Office officials to set up meetings with foreign officials and politicians, in a major change to protocol.
Mr Hunt said he would no longer sign off on help for trips that "give a platform for independence".
"I believe in the Union with every fibre of my being and British government policy is to protect, preserve, cherish and enhance that Union," the Foreign Secretary told the Daily Mail.
"So we are not going to offer support to Nicola Sturgeon if she goes abroad to drum up support for independence, and that is exactly why I am the Prime Minister that she least wants because she knows I won't allow our Union to be broken up."
That will now be restricted to trips touching on "areas for which [Scottish ministers] have a devolved responsibility" and where they "avoid supporting activities intended to campaign for policies contrary to [the UK] Government's position".