The education minister has written to councils advising them head teachers should instead exercise discretion.
Pupils are allowed to have up to 10 days away, but schools are judged on absenteeism rates.
Campaign group Parents Want a Say said the advice was a "terrific result".
Nearly 2,000 people signed a petition after hundreds of parents were fined over term-time holidays.
In his letter to councils on Wednesday, Huw Lewis said he was concerned some councils were advising "head teachers should not exercise their discretion and should instead refuse all requests for term-time absence as a matter of course", regardless of the circumstances.
"This is contrary to the regulations which allow a margin of discretion for the school in such matters so that each request can be considered fairly and on its merits," the minister wrote.
A BBC Wales Freedom of Information request in 2015 found wide variations in policy of imposing fines.
While Cardiff council issued 370 fixed penalty notices between January and May, 10 other councils did not issue any.
After receiving the petition in December, petitions committee chairman, William Powell AM, wrote to Mr Lewis saying some parents may have been dealt with unfairly and unlawfully.
He welcomed the minister's response, saying some councils had been "engaging in a cynical game of 'pass the parcel' on this issue".
"It is clear that the minister's intention, contrary to what applies in England, is for the discretion of individual head teachers to be respected," Mr Powell said.
"The Minister's response to the petitioners, in the light of compelling evidence received, is, in my view, a victory for common sense."
Craig Langman, chairman of campaign group Parents Want a Say, said it was a "terrific result" for parents in Wales.
"We hope this will encourage Westminster to reconsider its position on the policy in England," he added.
Campaigners who petitioned against parents being fined for taking term-time holidays are claiming a victory after it was agreed a blanket ban breached regulations.