The Dwyfor Meirionnydd AM is understood to have told his local party on Friday that he will sit as an independent AM in the Assembly.
The former Presiding Officer had previously been disciplined by Plaid leader Leanne Wood for criticising party policy.
Plaid Cymru said they would call for a by-election as soon as possible.
A party spokesman said Lord Elis-Thomas, who led Plaid from 1984 to 1991, had "misled" constituents.
A statement from the party said: "Plaid Cymru will begin the process of selecting a new candidate in Dwyfor Meirionnydd following Dafydd Elis-Thomas's decision to leave the Plaid Cymru Assembly group.
"Constituents, who Dafydd Elis-Thomas misled in the recent Assembly election, will expect a by-election to be held at the earliest convenience."
A spokesperson for the party's Dwyfor Meirionnydd constituency committee said: "We thank Dafydd Elis-Thomas for his work for the party and the constituency since 1974.
"We are saddened and disappointed by his departure.
"The local constituency committee now appeals to his conscience and requests that he stands down in order to allow for a byelection."
Lord Elis-Thomas has been asked to comment.
He has been an assembly member since 1999, previously serving as an MP since 1974.
In 2014, Lord Elis-Thomas lost the chairmanship of an assembly committee for criticising Ms Wood's spring party conference speech in which she said a vote for UKIP was "a vote against Wales".
Lord Dafydd Elis-Thomas has quit Plaid Cymru to become an independent AM, BBC Wales understands.