Alun Davies, who has responsibility for broadcasting, warned Wales had a "weakening" media and a lack of accountability was partly responsible.
But he stopped short of calling for devolved powers over the sector, during a media conference speech in Cardiff.
"I worry, and I am concerned, that Wales has a weak, indigenous media that is weakening," he said.
"And I am concerned that we don't always have the structures to enable us to have a conversation, apart from informally.
"The formal structures of accountability, formal structures of regulation and the formal structures to actually deliver policy.
"I think that is something which we do need to recognise, and is something that we need to debate and discuss.
"Not simply within government, or within the National Assembly, but within and throughout our society."
Mr Davies called for the assembly to have a greater role in holding media companies to account.
"I make no case for the devolution of responsibility for broadcasting to Wales or to the Welsh Government," he added.
"However, I do make the case for the accountability for broadcasting to be shared across the institutions of the United Kingdom."
Media bosses do give occasional evidence to assembly committees examining the media in Wales, but there is no formal arrangement that requires them to appear or submit evidence.
Since the renewal of the BBC's charter, the Welsh Government has been given a stronger role in appointing the Wales representative to the BBC board.
It used its veto to oppose the appointment of the UK government's choice for the position, Dr Carol Bell, earlier this year.
Dr Ruth McElroy, a media lecturer at the University of South Wales, said Wales' traditional media had weakened as the industry adapted to changing audience habits.
She told BBC Wales: "We have seen a great deal of closures of local newspapers. That's been a long-standing theme, and it's been greater in Wales than in the rest of the UK.
"I think what we have to do is be realistic that we are now in a digital age, and that modes of news delivery might be different in the future."
She added ministers should be more prepared to intervene to support media in Wales.
"There definitely is a place for government intervention. I think that sometimes, in the UK, we have been hostile to that, almost ideologically.
"In other parts of the world they are not, and they are reaping the benefits as a result."

Cameron Lancaster, from Burntisland, Fife, died on Sunday evening.
His family described his death as a tragic accident and "a great loss" and said Cameron would be hugely missed by family and friends.
The emergency services were called to Prestonhill Quarry near Inverkeithing at about 17:00 on Sunday and a body was recovered four hours later.
Police Scotland said inquiries are under way to establish the full circumstances of what happened, but it is thought the incident is connected to the ice bucket challenge.
A statement from Cameron's family added: "During his short life, he touched so many people with his friendliness, kindness and thoughtful generosity of spirit."

The animals were turned back from ferries at Larne and Belfast in the run up to Christmas.
Several investigations are now under way.
Some of the animals were voluntarily surrendered to animal welfare officers. Others were returned to the premises they had come from.
A total of 760 vehicles were stopped and searched at the two ports.
The joint operation involved officials from the Department of Agriculture and the Environment and several councils.
It was mounted following concerns regarding potential illegal movements of commercial consignments of dogs.
It focused on the welfare of the animals during transport, the identification of the animals and the licensing and registration of dog breeding businesses.
In the case of dogs moving from the Irish Republic, checks were also made that they had pet passports and complied with relevant trade requirements.
As part of the investigations, information will be shared with enforcement bodies in Great Britain and the Irish Republic.
Agriculture Minister Michelle McIlveen said the operation showed the illegal movement of dogs through Northern Ireland's ports would not be tolerated.
Media companies should be more accountable to the National Assembly, a Welsh Government minister has said.
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The death of an 18-year-old man in a flooded quarry is believed to be linked to the ice bucket challenge craze.
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More than 30 dogs have been stopped from being transported from Northern Ireland ports in an operation to prevent puppy trafficking.