“I am now very sad to have to report that she has died as a result of her injuries,” West Yorkshire Police chief Dee Collins told reporters.
Cox was pronounced dead at 1:48pm (1248 GMT), Collins told a press conference in Wakefield, northern England.
The attack happened in the village of Birstall, near Wakefield, in Cox’s constituency.
Police have arrested a 52-year-old man.
“We are trying to establish what we do know about this gentleman,” said Collins.
“At the moment the enquiries have just started.
“We are not in a position to discuss any motive at this time,” she said, but added: “We are not looking for anyone else in connection with this incident.”