It predicted that prices would have to rise 1% between 2016 and 2020.
That is on top of an increase of 5% it expects to have to make as a result of general wage inflation.
The Living Wage means that the minimum wage will be set at £7.20 an hour for over-25s from April 2016, which is forecast to rise to £9.35 in 2020.
The prediction came with Next's half year results - pre-tax profits came in at £347m, up 7% from the same period of 2014.
Earlier in the year, the company's shares fell after it issued a cautious sales outlook, predicting they would grow between 1.5% and 5.5%.
In the first half, total Next group sales were up 2.7% compared with the same period of 2014.
On Wednesday, the Institute for Fiscal Studies (IFS) published some research into how far the National Living Wage (NLW) would offset the cuts in benefits and tax credits announced in the 2015 Budget.
It found that families with someone in paid employment that are eligible for benefits or tax credits would lose an average of £750 a year as a result of the changes.
The IFS estimates that this group of 8.4 million working-age households will gain an average of £200 a year from the NLW.
It says this is an optimistic estimate because it assumes that the NLW will have no effect on GDP, employment or the number of hours worked.
Those averages also mask the differences in effects on different income groups. The IFS estimated that households in lower income groups would lose more as a result of the tax credit and benefit changes but gain less as a result of the NLW.
The retailer Next has set out the effect it thinks the government's National Living Wage will have on its prices.