Claire Hanna is also quitting as the party’s Brexit spokesperson.
The South Belfast Assembly member, who is a vocal critic of the link-up with Ireland’s main opposition party, will remain a member of the SDLP.
Ms Hanna, who has enjoyed a rapid ascent through the party ranks and was seen by many as a potential future leader, believes the alignment with a traditionally conservative party is inconsistent with the SDLP’s social democratic principles.
The Fianna Fail link-up was endorsed by more than two to one of SDLP members who attended a special party conference in Newry, Co Down on Saturday.
Ms Hanna supported a defeated motion that opposed the exclusive relationship with Fianna Fail and instead advocated a broader approach to political collaboration south of the border, incorporating other parties such as Fine Gael and Labour.
Announcing her decision on Twitter, Ms Hanna said: “Following the conference on Saturday, I have thought long and hard about the outcome and implications.
“I remain unconvinced that an exclusive partnership with Fianna Fail is the right vehicle with which to deliver the non-sectarian, transparent and social democratic new Ireland I believe in.
“As such, after a discussion with Colum Eastwood (SDLP leader), I have resigned from my position as SDLP Brexit spokesperson. This hasn’t been an easy decision.
“I remain an SDLP member and MLA, and will be continuing to work hard for the people of South Belfast and alongside SDLP members and activists, with whom I still share political values and aspirations.”
An SDLP spokeswoman said Ms Hanna had resigned as Brexit spokesperson and from the party’s Assembly group.
Reacting to Ms Hanna’s decision, Mr Eastwood said: “At the SDLP special conference all members were afforded the opportunity to speak and delegates to vote on two motions.
“The SDLP membership overwhelmingly voted for the party to embark on a partnership with Fianna Fail.
“It is with regret that we accept Claire’s resignation.
“The party membership has democratically spoken and, difficult though that decision may be for some, their wishes must be respected and enacted.”
On Saturday, Mr Eastwood hailed the birth of a policy partnership he said would build for a better future in the years ahead.
Within 24 hours, the chairpersons of the SDLP’s youth, women and LGBT+ wings said they were stepping down in an open letter that was sharply critical of how the decision was reached.
Matthew Corr (youth), Caoimhe McNeill (women) and Matthew Carson (LGBT+) wrote: “Calls for respect and party unity ring hollow when a coach and horses has been driven through the proper procedure which exists to facilitate a debate, on equal terms, and allow the party to come together after.”
They claimed Saturday’s conference was called without proper notice being given.
“Voting opened while the debate was ongoing, allowing people to vote before they had heard all points of view,” the letter said.
“This was extremely discourteous to speakers of every side.
“There can be no reasonable debate when the terms of the debate are arbitrary and extra-constitutional.”