Normal refrigerator water filters do not remove fluoride. There is almost no way to remove fluoride in the refrigerator because these types of filters are not made for refrigerator water systems.
There is no necessity for fluoride in the human diet and it can actually be somewhat detrimental to humans who continue to consume it. Infants should never be exposed to fluoridated water and it is recommended that tap water never be used for infants, especially in areas where fluoride is added to the water in the system. It is a good idea that parents of new babies check with their local water authorities to determine whether the water has had fluoride added to it.
For people who live in areas that have fluoride added to the water, it is important to find a way to remove the fluoride from the water before giving it to a new infant. Bottled and purified water can be purchased and used, but that can be environmentally detrimental. There are filters that are able to remove the fluoride, but parents should be sure that they purchase one that is specifically intended for removing fluoride. Osmosis filters, deionizers and activated aluminas are all able to remove fluoride from water; other filters are not effective at removing fluoride from water and should not be used for that purpose.