An exact timeframe for cheaper fares was not known, but Genter said she hoped to introduce them before the next election.
Transport officials would present several options for cheaper fares to her, which could include discounting each fare or giving low-income commuters a monthly allowance for public transport.
The zone system, which charged more for commuters who lived further away, could also be altered for Community Services Card holders.
Auckland Mayor Phil Goff said council modelling showed that halving fares for Community Service Card holders would lead to an extra 1.9m passenger trips a year in the city. The council decided against the discount because it was not affordable, but he fully supported the Government investigating the issue.
in September, the council will introduce free bus, train and ferry fares for children under 16 on weekends.
Mangere Budgeting Service Daryl Evans welcomed the Government's announcement. He said families in his area were struggling with living costs, and some were paying 60 per cent of their income on rent. They were left with an average of $39 a week for groceries, he said.
He said students in South Auckland often decided against tertiary study or dropped out of courses because the cost of travelling into the city was too high.
Genter said university lecturers had told her that students had been asking which classes they could miss because they could not afford to travel into the CBD every day.
"Between 2013 and 2017 the average weekly expenditure on public transport services among people in the lowest income group increased by 63 per cent," she said. "We know that increasing transport costs hit households on low incomes the hardest."
She said $4.6 million in 2019/20 would be used to cover the cost of operational systems needed to implement the scheme, depending on the outcome of initial investigations.
Potential sources of funding for the cost of fare concessions were still being explored, Genter said.
She said the scheme reflected the commitment in the Confidence and Supply Agreement between the Green Party and the Labour Party to investigate a Green Transport Card.
Community Services Card holders include people who receive a benefit from Work and Income. Approximately 16 per cent of tertiary students hold a card because they already receive a student allowance.