"We are suspending all campaigning for the day. Our thoughts are with Jo Cox and her family," the Twitter page of the campaign said.
Local police reported is had arrested a 52-year-old man suspected of the attack.
Following reports on the incident, UK Prime Minister David Cameron, London Mayor Sadiq Khan and former head of the UK capital Boris Johnson have expressed support to Cox and her family.
UK nationals are set to vote on June 23 in a referendum on the country's EU membership.