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.

The 42-year-old Tasmanian has spent two years as assistant coach and lead batting coach for Cricket Australia.
Di Venuto was with Sussex and Derbyshire before moving to Durham, where he twice won the county title.
But he is scheduled to return to England in time for the new season in April on an initial three-year deal.
Surrey director of cricket Alec Stewart said: "Following the departure of Graham Ford it was vitally important that we found another high quality coach with a great work ethic and excellent knowledge of the English county game.
"Michael is a good people person. His 12 years of county experience will be invaluable. He is highly regarded within the Australian set-up for his ability to work with and get the best out of players.
"Being able to appoint a coach from a top quality international team can only serve to benefit the club and I would like to thank Cricket Australia for their professional dealings."

In the past year more than 90% of girls aged between 12 and 13 have had the treatment, an NHS spokeswoman said.
The vaccine, which consists of three injections over a six-month period, is given in secondary schools and at community clinics.
HPV causes most types of cervical cancer.
Dr Lincoln Sargeant, consultant in public health medicine at NHS Cambridgeshire said: "We are very pleased with the response to the HPV vaccination programme across the county.
"In the UK cervical cancer is the twelfth most common women's cancer."
More than £31m is required to treat patients who have been waiting more than a year for some appointments, the health minister has said.
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Surrey have appointed former Australia one-day international batsman Michael di Venuto as their new head coach to replace Graham Ford.
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NHS Cambridgeshire has said it is "very pleased" with the number of girls having the vaccination against human papilloma virus (HPV).