It follows a recommendation from the Women’s Health Taskforce, established by the Department of Health in 2019 to improve the standard of women’s healthcare.
The centre is to be established this year and will be located at the National Maternity Hospital in Dublin.
Mr Donnelly said he expects that other such clinics will be established around the country.
He said: “One area that has received considerable attention this year, quite rightly, is menopause, and the lack of any specialist centres for menopause. It’s kind of extraordinary that it has never been in place.
“I’m delighted today to be able to announce that we are establishing the first specialised menopause clinic in the public health system.”
Speaking at the Fianna Fáil think-in in Cavan on Friday, Mr Donnelly said he would seek funding through the budget for the project, to give the issue “attention that it rightly deserves”.
He added: “The clinic is going to be multidisciplinary. It’s going to have GPs, who are specialising in this area, and clinical nurse and midwife specialists, which is really, really important.
“It’s one of many priorities Fianna Fáil has and the Government has for women’s health care.”
He said a range of other initiatives would also be brought forward, on the back of recommendations from the taskforce.
“I just want to acknowledge the ongoing work from the Women’s Health Taskforce. They’ve been engaged in a radical listening exercise and the results coming in from that are very, very interesting and are really informing our women’s health plans as we go on.
“We’re also funding the development for the delivery of training of long-acting reversible contraception, for 45 GP trainees and 50 postgraduate GPs per year.
“We’ve already funded a lot of other initiatives. We are expanding nine gynaecology clinics. We are establishing this year two fertility clinics at hubs in Nenagh and in Galway. We funded an additional 24 lactation consultants, and a specialist endometriosis service in Tallaght University Hospital.”
Junior minister Mary Butler also spoke about efforts to improve perinatal mental health services this year, with six hubs, 13 spoke sites and 13 specialist nurses now available.
Ms Butler said: “Regardless of where you live, regardless of which maternity hospital you present to, if you do have ill mental health, before, during or after your pregnancy, you can get the support of a specially trained mental health nurse.”