Barnsley Council in South Yorkshire announced term dates for academic year 2017-18 with a shorter summer break.
There will be a longer school holiday at October half-term.
Nick Bowen, principal of Horizon College, said the cut would "lead to difficulties in recruitment and retention of really good staff".
Councillor Tim Cheetham said: "The main differences to this year's dates from previous years will support educational outcomes for pupils by reducing the long summer break which can lead to learning loss.
"It also means that holiday weeks are distributed more evenly throughout the school year"
The 2018 summer holiday is to run from 31 July.
In 2017, schools are to break up almost a week earlier on 26 July.
This year the final day of term is to be 20 July, according to the council website.
Barnsley has 78 primary schools, 31 of which are academies, for children between the ages of five and 11. There are 10 advanced learning centres, four of which are academies, for 11-18-year-olds, said the council.
Mr Bowen said: "Half of Barnsley will be operating under this new system the other half, the academies, many of them are saying they're not going to do it."
Simon Murch, of the National Union of Teachers, said: "It seems a very poorly-thought-out idea.
"Anything that changes the system we've got at the moment that works really needs to be thought out."
The council said it had consulted teachers and parents on the changes.
Mr Murch said the union thought the consultation was continuing and no decision had been reached.
Parents have also commented the move on BBC Look North's Facebook page.
Colleen Bell said: 'I love the long summer break with my kids. Plus what a nightmare for parents with children in different schools or colleges that aren't doing this."
Sue Walker said: "Keep your thieving hands off my time with my kids. I'm already being told when I can and cannot go on my holidays with them, and now you want to cut short my holidays."
Claire Sutton supported the move, she said: "I think limiting the summer to four or even five weeks would be a good idea. An extra week or two somewhere else gives parents flexibility with regards to holidays and childcare."
A council has announced a cut in the school summer holidays to under five weeks, bringing criticism from some parents and teachers.