Bialik broke the news on the parenting website Kveller.
"After much consideration and soul-searching, Michael and I have arrived at the decision to divorce due to 'Irreconcilable Differences,'" the actress wrote. "Divorce is terribly sad, painful and incomprehensible for children. It is not something we have decided lightly. ... We will be ok."
She and Stone are the parents of sons Miles, 7, and Frederick, 4.
The actress is best known for her roles on TV's "Blossom" and "The Big Bang Theory."