Firefighters were called out after a carbon monoxide alarm went off in Kingsquarter at about 3.30am.
A crew from Maidenhead and the ambulance service also attended.
The residents, two adults and a two-year-old and a four-month-old baby, got out of the flat safely and did not need to go to hospital.
The firefighters ventilated the property and left the family in the care of the ambulance service.
It is not known where the carbon monoxide was coming from, but firefighters thought it could have been from building work.
Carbon monoxide is an odourless, colourless gas that is very difficult to detect and inhaling it can be fatal.
Deputy crew manager Paul Studwicke said it is important people have carbon monoxide indicators fitted.
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