Jo Cox, a mother of two, was left bleeding on the pavement after the incident in Birstall in West Yorkshire, media reports said.
A 52-year-old man has been after Cox was shot in Birstall.
West Yorkshire Police said in a statement, "At 12.53 today, police were called to a report of an incident on Market Street, Birstall, where a woman in her 40s had suffered serious injuries and is in a critical condition."
"Police presence in the area has been increased as a reassurance to the community," it said.