Edinburgh, East Ayrshire, Moray, Western Isles, Shetland, and Orkney councils are all falling short of targets on out-of-school childcare provision, according to data compiled by the Family and Childcare Trust.
Data for a further 10 local authorities, including Scotland's largest, Glasgow City Council, was unavailable.
The charity is publishing its findings for the UK as a whole before the start of the new term south of the Border.
The trust said working parents whose children have either started school for the first time in Scotland or are due to start next week face "an unprecedented battle to find out-of- school childcare". More than 60 per cent of local authorities in the UK say they do not have enough childcare, or they do not know whether there is enough childcare, for five to 11-year-olds.
More than 650,000 five-year-olds across Britain could be left without any out-of-school childcare in September, according to the Out of School, Out of Mind report.
According to the survey, more than 40 per cent of parents said their childcare arrangements became more difficult as soon as their children started school. Nearly two-thirds of parents (63 per cent) said they had been forced to change their working patterns when their children had started school, with almost 12 per cent having to either change or quit their jobs completely.
Anand Shukla, chief executive of the Family and Childcare Trust, said: "Far too many parents face a never-ending battle to secure affordable, quality childcare."
The report comes weeks after it emerged that hundreds of parents have been unable to secure free childcare places in their chosen nurseries.
Under new SNP legislation, families are entitled to a mandatory 600 hours of funded early learning and childcare for three- and four-year-olds. However, a survey by campaigning parents from Glasgow revealed there was a shortfall of 583 places in the city.