The Progressive Conservatives had tabled a reform bill last year, but it died with that last session.
The federal government has since asked the Supreme Court of Canada to rule on whether changing the Senate requires changing the constitution.
Deputy Premier Paul Robichaud said there is no point passing a bill before Canada's top court rules on the question.
"We're going to wait to see the decision of the Supreme Court and after that, we'll move on with a new piece of legislation if we need to do so,” he said.
Premier David Alward's Senate reform proposal would have New Brunswickers vote on which names should be submitted to Ottawa for appointment to the Senate by the prime minister.
When Alward unveiled the legislation last year, he called the Senate reform proposal "historic."
He said the first Senate elections would likely be held in 2016.
New Brunswick has 10 seats in the upper chamber.
Supreme Court hearing
But that’s on hold until the Supreme Court rules on whether all provinces, or just a majority, must agree on Senate elections and term limits, or on the abolition of the Senate altogether.
It is also considering if Ottawa can legislate those changes itself.
Justice Minister Marie-Claude Blais said the provincial government has yet to develop its legal position on those points.
"When the time comes, I'll be more than happy to sit down with you and talk about that,” Blais said.
All provinces have been given intervener status in the Supreme Court hearing, which is scheduled for three days this fall.
The ongoing scandal over Senate expenses has prompted many Canadian politicians to talk openly about the need for reforming or abolishing the Senate.
Ontario Premier Kathleen Wynne said on Wednesday that she'd like to see the upper chamber reformed.
Meanwhile, Senator Marjory LeBreton, the government's leader in the Senate, said this week the Senate should be abolished if it cannot be reformed.Suggest a correction