Men and married couples, on average, will need 9 percent more in savings than a year ago to pay for healthcare, while women will need 16 percent more in savings for healthcare than last year, the institute concluded.

Male Medicare beneficiaries with supplemental insurance such as Part D or MediGap will need $86,000 in savings for retirement health costs, while women in a similar situation would need on average $125,000 in retirement, because of their longer life spans. A couple with average drug and medical expenses would need about $210,000 in savings.

This nest egg would give retirees about a 50-50 chance of being able to afford their healthcare. To have a 90 percent chance that all healthcare costs would be affordable over the course of retirement, couples would need savings of upward of $807,000, in addition to Medicare and supplemental insurance, according to the report.

Many retirees will need even more money than these estimates because they exclude long-term care expenses and other basic living costs such as shelter and food, according to the report.