The money would ensure anyone waiting 12 months to either see a consultant or start treatment by March 2017 would be seen and treated by March 2018.
Michelle O'Neill said she was confident the money would be agreed after the election on 2 March.
She told BBC News NI she believes the plan is achievable.
The minister published her strategy to tackle hospital waiting lists on Tuesday.
The minister revealed that £1m is being invested in the private sector in order to start tackling waiting lists immediately, although this is not detailed in the action plan.
While welcoming the announcement of the plan, the DUP's health spokesperson Paula Bradley said improvement on waiting lists was being hampered by the lack of a budget and election demands.
"Progress was being made on waiting lists previously," she said. "At the start of 2016, figures for both outpatient and inpatient waiting times were coming down and we need to see a continuation of that kind of progress."
Jo-Anne Dobson from the Ulster Unionist Party claimed the health minister was "engaging in a pre-election stunt."
"Michelle O'Neill is right to say that when she took up office last May lengthy waiting times were a major problem," she said. "Yet under her watch those delays have only worsened."
The SDLP's Nichola Mallon said patients who are waiting for procedures would want to know what the strategy means for them.
"We need to know when people are going to be treated and have cast iron guarantees that the money is going to be there," she said. "Unfortunately we don't have those guarantees."
Paula Bradshaw, the Alliance Party's spokesperson on health, said more detail and further scrutiny was required.
"It is concerning the lack of a Budget means the allocation of funding which is needed to achieve what the plan sets out to do remains unclear," she said.
More than £31m is required to treat patients who have been waiting more than a year for some appointments, the health minister has said.