The government measure will mean the minimum wage for over-25s will rise in April 2016 from £6.70 an hour to £7.20.
Experts say it will have a major impact in the social care sector, where much of the workforce earns minimum wage.
The department said the hourly rate paid to providers would "inevitably have to be reviewed".
It is not yet clear how much extra money is needed or where it could come from.
A report by the Commissioner for Older People for Northern Ireland (COPNI) found the average hourly tariff paid for home care in Northern Ireland is £11.35.
That tariff, which must cover workers wages and all other costs, is the lowest of any part of the UK.
The body that represents private and voluntary sector care companies has described that as inadequate, even before the National Living Wage is introduced.
Pauline Sheppard, the chief executive of Independent Health and Care Providers, said some firms feared their businesses would no longer be viable.
She described the National Living Wage as a "positive" measure that would see care workers "recognised and rewarded".
"The difficulty is if it's not going to be funded through from the trusts and the Department of Health," she said.
She said "the market will fail, and fail quite soon" without an increased tariff.
The department said it was in discussion with the Health and Social Care Board about the financial impact of the National Living Wage on the delivery of services, including home care.
It added: "In recent discussions with independent sector representatives, the board has invited them to submit information which would help to inform these discussions."
COPNI has recommended that the department commissions a health economist to determine the accurate cost of home care, something that has never been done in Northern Ireland.
The Department of Health has indicated it could make more money available to the home care sector to deal with the impact of the National Living Wage.