Police officers should not be used as "factory inspectors" to enforce social distancing rules, the North Wales Police and Crime Commissioner (PCC) Arfon Jones has said.
Regulations that came into law on Tuesday allow police and councils to fine firms for not doing all they can to keep workers two metres apart.
But Mr Jones said all four Welsh chief constables have objected to doing so.
But the Welsh Government said police enforcement is only a "last resort".
Dyfed Powys police chief constable Mark Collins said his force does not have the capacity to enforce it.
The Plaid Cymru politician, who otherwise supports the legislation, said: "The chief constables have urged the Welsh Government to change their guidelines as a matter of urgency and I am standing shoulder to shoulder with them on this."
Under the law, police and councils have powers to issue fixed penalty notices ranging from £60 for a first offence, to £120 for a second and subsequent offence.
There has been criticism that the fines are too low, and that the way the law was introduced has put companies into difficulty.
First Minister Mark Drakeford has also said the rules are not an "absolute ban" on people working closer than two metres - with companies expected to take reasonable measures to ensure the health of their staff.
He has said the law would be largely self-policing, with workers raising concerns themselves.
Mr Jones, who oversees the budget and sets the objectives for North Wales Police, said: "I support the legislation but I am totally against the idea of it being enforced by the police.
"It is like using police officers as factory inspectors when North Wales Police and the other Welsh forces have important work of their own to do during the coronavirus crisis."
He said the Health and Safety Executive and local authorities "should step up to the mark here and do their job".
"They should take responsibility for enforcement rather than expecting the police to do their job for them," he said.
"I am sure the public of north Wales would far rather that our police enforce essential travel legislation rather than have them visiting factories to ensure that employees are kept two metres apart, which is surely what the Health and Safety Executive should be doing," he said.
The Health and Safety Executive has not been named as a body that can enforce the legislation.
But Local Government Minister Julie James denied the Welsh Government was asking police to be "factory inspectors".
She told a press conference workers who want to raise concerns should first tell their employer, and contact their trade union if they have one.
"If that doesn't work, and it will work in the vast majority of cases, contacting your local authority trading standards department or raising it with your local assembly member will also do the trick," she said.
"The police are obviously only a very last resort for recalcitrant employers really determined to break the rules. We do not expect to have any of those in Wales."
BBC Wales contacted all Welsh police forces for a response.
Dyfed Powys Police chief constable Mark Collins said: "Along with my counterparts across Wales, we are speaking with the Welsh Government in relation to the enforcement of this change of legislation.
"We do not have the capacity to enforce this and believe it's a matter for the Health and Safety Executive and local authorities."
Alun Michael, PCC for South Wales, said: "It's very welcome that Welsh Government have made clear the expectations on employers at this time through the legislation.
"It is important that the Health & Safety Executive, which has responsibility for workplace safety, now use this opportunity to reinforce what any good employer will be doing any way through the current crisis."