Members of the community say the opening times for the new centre will make it difficult for people to use the facilities before work.
And they fear families will not be able to make the most of the new pool due to limited weekend hours.
Matt Thomas, who lives in the South Kirkby area, said: "The timetable provides not a single day where the pool or other facilities open prior to 8am, meaning anyone wanting to nip for a swim or to the gym before work, after a night shift or before setting out on a school run can’t do so.
"Weekends are even more ridiculous - the centre will close at 2pm on both Saturday and Sunday, the days when families have no school to get in the way of special family time and when many workers enjoy at least one full day off."
Mr Thomas has written to the council to ask for the timetable to be revised. He describes the timetable as "frankly absurd".
Wakefield Council revealed last week that the centre, which includes a gym and swimming pool, will open from 8am until 9pm Monday to Thursday, 8am until 8pm on Fridays and 8am until 2pm on weekends.
Posting the fitness and swimming timetables on Facebook, the authority said: "We are keen to make sure our classes and timetables reflect what our customers want, and expect to develop these over the coming weeks and months. In the meantime, if you have any comments please let us know."
Several frustrated residents responded to the public post.
Beth Atkinson wrote: "In my opinion I think you should have more of the public swimming after 2pm on a Saturday and Sunday due to the fact that’s the only time people get to take their kids swimming. I for one cannot use it through the week with children due to work so it was a big let down to see that you close at 2pm on a weekend when families will use it most."
Wendy Green agreed, adding: "Great for people that don't work and don't have kids. Really late opening so no chance of going before work. Swimming times are really poor, and weekend hours are terrible!"
And Tiffany Watson said: "Be nice if some classes were earlier so you could still do a class, get showered and go to work."
Karen Collins, service director for culture and sport at the council, said: "This is just an initial timetable that we will happily adjust if there is customer demand. We’ll be encouraging all our Minsthorpe leisure customers to let us know their views when they come to centre so that together we can develop a timetable that meets the needs of as many people as possible."
The new leisure centre will officially open on Thursday.
Olympian Max Litchfield who learnt to swim at the old Minsthorpe Pool will make an inaugural swim with three of the district’s medal winning swimmers Keiran Swift, Steve Scott and Mathew Gay, who competed in the 2017 Special Olympics, for athletes with intellectual disabilities.
Council leader Coun Peter Box will do the grand opening - and people can begin to use it from 3pm.