Lord Hain told the BBC's Sunday Politics Wales programme he had never been as concerned as he was now about the party's prospects.
He said it was "much more serious" than the "early 1980s strife".
Jeremy Corbyn has been urged to stand down as Labour leader by most of his MPs, with Angela Eagle and Owen Smith considering a challenge if he refuses.
Lord Hain spoke of his experience as a leader of Welsh Labour's doomed referendum campaign for a vote in favour of remaining in the EU.
Voters in the party's traditional heartlands of south Wales contributed to the overall majority for Brexit.
"What is very clear is that a whole group of citizens in those valleys who almost to a person used to vote Labour feel left behind," the former Neath MP said.
"It's a very dangerous moment for us.
"What we have to do is reform, re-found our party in the communities - but not in the old institutions that have disappeared, the trade unions and the clubs."
Amid calls for Mr Corbyn to resign to help Labour recover, he said: "We can get out of it... if we had credible leadership.
"Then I think we can win, even including an early general election."
However on Friday, Labour AM Mike Hedges said opponents of Jeremy Corbyn need to "put up or shut up".
Mr Hedges reiterated his support to the Labour leader, calling for opponents to stand against him if they think they can do a better job.
Labour is in "a major crisis" and has lost touch with its voters, a former Welsh Secretary has warned.