Jo Cox |
Detectives are investigating whether her killing, outside her constituency office in Yorkshire, was politically motivated.
Suspect Tommy Mair, 52, was detained by police near his home in Birstall, West Yorkshire.
Prime Minister David Cameron suspended campaigning in the European Union referendum after the tragedy. Britons are due to vote on Thursday.
Cox, a 41-year-old mother of two, represented Batley and Spen in Parliament. She won the seat for the Labour Party in May last year, was a popular figure in Parliament and a passionate human rights advocate.
Cameron, on a campaign-related visit to Gibraltar, expressed his condolences to Cox's family.
"This is absolutely tragic and dreadful news. My thoughts are with Jo's husband Brendan, their two children and their wider family," he said.
"People are going to be very sad at what's happened, at this dreadful news, and it's right that we've suspended campaigning activity in this referendum."
Cox was active in the Remain campaign. Labour leader Jeremy Corbyn said in a statement, "The whole of the Labour family, and indeed the whole country, is in shock and grief at the horrific murder of Jo Cox.
"Jo was dedicated to getting us to live up to our promises to support the developing world and strengthen human rights — and she brought those values and principles with her when she became an MP."
Alan Mak, an MP and the first person of Chinese and East Asian origin to be elected to the House of Commons in Britain, said on Friday:"Jo Cox was an outstanding MP and colleague in Parliament. She was warm, passionate and a strong voice for her constituents. Her death so young is a tragedy."
Cox is survived by her husband and two young children.
In a statement on Thursday, her husband said, "She would have wanted two things above all else to happen now. One, that our precious children are bathed in love. Second, that we all unite to fight against the hatred that killed her. Hate doesn't have a creed, race or religion, it is poisonous."
Yan Jin, vice-president of the School of International Studies at Renmin University, said, "It's just one week before the referendum, and the killing may impact the outcome as some people, especially those without strong opinions on staying in or leaving, may vote out of sympathy.
"But we should also consider it as an individual case, which may not influence the final outcome to any great extent."
Wang Mingjie in London and Yan Dongjie in Beijing contributed to the story.