The department also estimates it will cost up to €5 million to keep Covid-19 out of jail.
They recently published a briefing document that has been prepared for Justice Minister Helen McEntee.
It says anecdoctal evidence indicates about 70 per cent of prisoners present with mental health issues.
It also says overcrowding remains a big issue for the Irish Prison Service.
There was a 10 per cent increase in the number of people in custody between December 2016 and December 2019, with a 50 per cent increase in women in jail.
Additional Covid-19 related costs in prisons are likely to cost up to €5 million.
The department says another financial challenge facing the Irish Prison Service is compensation claims over a lack of in-cell sanitation.
A former prisoner got €7,500 in damages last year after he sued over having to 'slop out' in his cell - and the state faces many similar claims.