Butcher took charge at Easter Road last November, leaving his role at Inverness Caledonian Thistle to take the post, but oversaw Hibernian's demotion by virtue of a play-off defeat to Hamilton in May.
The former England international defender won just four of his 25 regular-season games at Hibs, and he has subsequently been relieved of his duties.
In a statement released on the Edinburgh club's website, chief executive Leeann Dempster said: "I have to say that we all regret that this decision had to be made, but during conversation it became clear that a different approach was needed.
"Sadly, for a variety of reasons and perhaps including unfortunate timing, it hasn't worked out for Terry here. That is disappointing for all concerned. I am genuinely saddened that we have had to take this tough decision.
"It may have taken longer than we all would have liked but I felt it was appropriate that we met properly and had a full discussion before any decision was made.
"Now we need to move forward and act to bring in a new manager with the aim of getting us promoted back to where Hibernian belongs, in the top league of Scottish football, from a uniquely competitive Championship.
"Our first aim must be to try to win the league and gain promotion automatically.
"The search now begins to find and appoint the next manager."
