Osbourne defended broadcaster Piers Morgan over his criticism of a high-profile TV interview given by the Duchess of Sussex.
That led to a clash with co-host Sheryl Underwood, who accused Osbourne of giving "validation" to "racist" views.
TV network CBS took The Talk off air while it carried out an investigation.
In a statement on Friday, CBS said the events of the 10 March episode "were upsetting to everyone involved, including the audience watching at home".
