She told community health council (CHC) members not to be "parochial" or to publicly oppose proposals being drawn up by health boards to change services.
It comes as a review is carried out of CHCs themselves, which the Welsh government says have a crucial role.
The Conservatives attacked Mrs Griffiths's "oppressive" approach.
With local health boards preparing to publish their plans for re-organising services, politicians have expressed fears that reforms could mean some hospitals are downgraded.'Campaign'
In a speech to CHC members, Mrs Griffiths said: "Community health councils cannot be parochial.
"You must consider the needs not only of the local population but of the whole Welsh health service. This has and will continue to present challenges to you.Continue reading the main story Daniel Davies BBC Wales political reporter
Lesley Griffiths says community health councils (CHCs) "cannot be parochial" and must consider the needs of the whole of Wales.
So how do they square that with their duty to their local patch?
CHCs were created to give the public a voice in how the NHS is run.
Each local health board has its own council, with members drawn from local authorities, nominated by voluntary groups or appointed by ministers.
Those members will be aware that in some communities there is deep anxiety about potential changes to the NHS. Protesters who fear the prospect of services being withdrawn from their local hospitals have held demonstrations on the steps of the Senedd.
And all this comes at a time when CHCs themselves have been subject to a review whose findings were originally expected last month.
Among other things, Mrs Griffiths asked the review to look at "what we are getting for our money" from CHCs. It's a "root and branch" review that could herald fundamental reform of a system designed to give the public a say in the running of the health service.
With big changes afoot for the NHS, the accusation against Mrs Griffiths is clear: she's telling CHCs to speak up for patients, but to do it in private."However, I am clear members of community health councils cannot sit in two camps.
"They cannot be a member of a council whilst at the same time campaigning against proposals in relation to service reconfiguration which the LHB might be considering."
She also warned members against divulging any "sensitive" information they might receive from health boards.
There have been protests outside the Senedd this year attracting thousands of people concerned about the future of their local services under the forthcoming reviews.
Christine Evans, chair of the Betsi Cadwaladr CHC, said she would continue to speak out for patients.
"We're all well-meaning people and everyone is doing their best for the health service, which we love very much.
"I've given my whole life to the health service and I'm not having somebody come along and telling me that I'm not allowed to speak out."
She added: "We are here, us volunteers, at the behest of the public.
"We are the voice of the patient and we are independent. We should be allowed to say what we feel."
Ms Evans, a retired surgeon, said changes to the NHS were necessary "but we need to do it considering everyone's feelings".
Tony Beddow, a professor at the Welsh Institute of Health and Social Care and a former NHS manager, said CHCs tried to represent their communities and "test out" arguments for change.
"They have the right and the ability to speak both with their local health services and with the political process in Wales."'Ultimatum'
Conservative health spokesman Darren Millar said: "As far as the health minister is concerned it's my way or the highway. That dictatorship must end now.Continue reading the main story
We are the voice of the patient and we are independent. We should be allowed to say what we feel”End Quote Christine Evans Betsi Cadwaladr Community Health Council "This is nothing more than an oppressive ultimatum which attempts to gag those individual members of community health councils and prevent them from voicing their concerns.
"The implication is clear: support reorganisation plans, no matter how unpopular or unsound they may be, or go."
But Carol Lamyman-Davies, director of the board of CHCs in Wales, said: "I don't think the minister was, in any way, trying to gag community health councils, they have an important role, a vital role.
"What the minister is actually saying was that it is inappropriate for community health council members to have a voice on a health lobbying group whilst also being a community health council member. And I think in that respect she was very right."
She said it was the duty of CHCs to reflect views but also working in patients' interests.
The first set of proposed changes from the NHS are expected next month from Hywel Dda and Betsi Cadwaladr health boards. Proposals for south Wales from Cwm Taf, Cardiff and Vale and Abertawe Bro Morgannwg health boards will be made public in October.
The minister is awaiting the results of a review into CHCs, and will then consider whether changes are needed. She has the power to remove members of CHCs.
A Welsh government spokeswoman said: "The health minister believes CHCs have a crucial role in working with LHBs on any changes to help get them right.
"She has reminded CHCs of their duty to act on behalf of the whole community and not focus on narrower parochial interests.
"Only in this way can trust between LHBs and CHCs be maintained and information shared freely before plans are finalised. Campaigning publicly against specific proposals by LHBs is incompatible with the role of CHCs, as set out clearly in their code of conduct."