Theresa May has resisted calling for the England team to boycott the event in Russia following the Salisbury nerve agent attack.
However members of the Royal Family and Government officials will not be attending.
The event, due to kick off in Moscow on June 14, is expected to be exploited by Russian president Vladimir Putin as a huge PR opportunity for his country.
However, Mr Kinnock said Fifa should be asked whether it was appropriate to mount a celebration of football in a state suspected of being behind the deployment of a nerve agent on British streets.
Mr Kinnock said: “I think we should consider making a co-ordinated approach to Fifa and talk about moving the World Cup to 2019.
“Putin has invested billions of roubles in the World Cup and sees it as an opportunity to showcase his regime to the world.”
The Prime Minister has said no Government ministers or members of the Royal Family will attend the tournament.
The Foreign Office has warned England fans they should “be aware of the possibility of anti-British sentiment or harassment”.