No, the Brita filter cannot remove fluoride from water. This isn’t a limitation of Brita filters in particular though, the vast majority of filters cannot effectively remove fluoride. While sodium chloride (the kind of fluoride added to tap water for dental hygiene) is a large molecule, it is also soluble which means that when mixed with water it becomes an aqueous salt many times smaller than what most filters are able to remove.
As the diagram shows, fluoride is one of the most difficult contaminants to remove. Reverse osmosis filters will absolutely do the job of filtering out fluoride but they’re also really big and bulky, waste a ton of water and require some minor plumbing work to install– far from a drop-in replacement for a Brita filter. Instead, I’d recommend either the ZeroWater or Berkey water filters. Both filters use a filtering technique called ion exchange which is one of the only general purpose filters besides reverse osmosis that can actually filter fluoride. Bone char and alumina filters are two other filter methods that can eliminate fluoride but I’ve excluded them because they are special purpose and have their own drawbacks.
To find out more about the best water filter, check out my article on how to filter microplastics from water.