Welsh Conservative leader Andrew RT Davies said he was baffled by Mr Jones’ comments.
Speaking to BBC Wales’ Sunday Politics Wales programme, Mr Jones said: “At the moment there are rules. There are EU state aid rules that govern what we can and can’t do.
“If there are no rules, it becomes a free-for-all. That’s a bad thing for any single market.”
EU state aid rules regulate how much help governments can give to local industries.
Mr Jones said an inability to set UK-wide trade rules after Brexit “could cost jobs, it could cost a lot of money – that affects ordinary people, and that needs to be resolved as soon as possible.”
Welsh Conservative Leader Andrew RT Davies said: “I’m baffled by his pronunciation of a trade war.
“As I last looked at the constitutional settlement, trade and industry certainly wasn’t devolved and international negotiation was not devolved.”
Mr Jones also told the programme that the battle to keep the United Kingdom together “will be lost” unless the UK government starts listening to the devolved nations.
“We can share power in the UK, we can still be stable, we can still have the union, but the UK government needs to realise this now otherwise the battle will be lost,” he said. “They need to wake up and smell the coffee.”
Senior party figures from across Britain, including former prime minister Gordon Brown, will attend the launch of the constitutional convention in Cardiff at the end of March. The first minister first called for a UK-wide constitutional convention five years ago.
Plaid Cymru criticised the announcement, adding that Wales needed its own constitutional convention.
Adam Price, the party’s economy spokesman, said: “Rather than the Labour party talking to itself, why doesn’t it talk to the rest of us?”
UKIP assembly group leader Neil Hamilton said he thought Brexit would lead to “more powers” to the devolved institutions.
Welsh Liberal Democrat leader Mark Williams welcomed the convention but said “there’s a much bigger question than what we’re being presented with at the moment and that requires an UK response”.