Marr, 53, hosts a popular eponymous Sunday morning show frequented by top British politicians and commentators, in addition to a Monday radio show called "Start the Week."
The BBC said in a statement Wednesday that Marr fell ill a day earlier and was taken to the hospital, where doctors confirmed he had had a stroke.
The BBC said Marr's doctors say the host is responding to treatment and that his family has requested privacy.
Marr began his career as a newspaper reporter, going on to become editor of the Independent before joining the BBC as political editor in 2000.
The BBC said guest presenters will host Marr's two shows in his absence.