No, nor should you waste your money on commercially available toothbrush “sanitizers” or special mouthwashes or disinfecting solutions.
Thoroughly rinsing the toothbrush with plain old tap water “does remove most of what’s caught there,” said Dr. Dana Graves, a professor of Periodontology and Oral Biology at the Boston University School of Dental Medicine. And leaving the brush uncovered so it can dry off between uses or using a toothpaste containing a disinfectant also helps reduce the amount of live bacteria and viruses on the brush.
It’s true that there are lots of bacteria, viruses and fungi that can linger on toothbrushes, but both the American Dental Association and the federal Centers for Disease Control and Prevention pooh-pooh the risk of re-infecting yourself by re-using the same brush. (You shouldn’t share a toothbrush with someone else, though, because they may have germs that your immune system is not revved up to defend against.)
The CDC notes that “no published research data documents that brushing with a contaminated toothbrush has led to recontamination of a user’s mouth, oral infections or other adverse health effects.” The dental association says “there is insufficient clinical evidence to support that bacterial growth on toothbrushes will lead to specific adverse oral or systemic health effects.”
You should get a new toothbrush or head for an electric toothbrush every three to four months, not for health reasons but because the bristles get frayed.