The oil and steel magnate had been treated as a 'new applicant' after his previous 40-month investor visa lapsed in April - effectively banning him from Britain and forcing him to miss Chelsea's FA Cup win a fortnight ago.
Britain's bitter row with Russia after the assassination attempt on Sergei Skripal means hundreds more oligarchs wanting their 'Tier 1' visa - dubbed the 'golden visa' because of the wealth needed to get one - must now demonstrate their cash is not 'dirty'.
Abramovich's decision to dump the £1billion project is hugely significant because he has spent 15 years pursuing his 'dream' to build Europe's best stadium for Chelsea.
The Daily Mail asked Chelsea and Abramovich for comment but they declined.
The Russian citizen's extraordinary wealth has transformed Chelsea's fortunes and earned the former Premier League and Champions League winners the nickname 'Chelski'.
Chelsea's official statement has said its 60,000-seat arena was put on hold 'due to the current unfavourable investment climate'.
Experts have suggested that pulling his investment could be the ultimate powerplay with the Home Office over his visa - but others say the redevelopment just doesn't stack up financially because it will cost £1billion to add just 19,000 new seats.
It could also mean he is set to sell his beloved Chelsea and quit Britain for good.
Mr Abramovich had been waiting for his 'golden visa', granted to foreigners who invest more than £2million in Britain every year.
Without one he cannot work for Chelsea and this week it emerged he will officially move to Tel Aviv to restore his access to the UK.
Relations between Moscow and London have been strained since former Russian double-agent Sergei Skripal and his daughter were poisoned in Salisbury in March.
Britain blamed the attack on Russia but the Kremlin denied any involvement.
As his father's family were Jewish, Mr Abramovich is entitled to live in Israel – and an Israeli passport would restore his access to Britain, as citizens can enter the UK without a visa.
Local news sites in Israel reported that Abramovich had flown into Tel Aviv this week and received documents confirming his status as an Israeli citizen.
And the Jerusalem Post says he has now pulled his UK visa application.
Israel grants citizenship to any Jew wishing to move there and a passport can be issued immediately.
Israeli passport holders can enter Britain without a visa for short stays although they would still require visas to work here.
Abramovich has been a regular visitor to Israel and Ynet said he had bought a property that was formerly a hotel in an old Tel Aviv neighbourhood close to the Mediterranean.
Chelsea has said there is no time frame for the reconsideration of their stadium decision.
There is also uncertainty of manager Antonio Conte, who could be sacked or move to the newly vacant Real Madrid job.
Some have suggested that Mr Abramovich could consider slowing his spending at Chelsea and could consider selling up.
After today's shock stadium decision Chelsea said in a statement: "Chelsea Football Club announces today that it has put its new stadium project on hold. No further pre-construction design and planning work will occur.
"The club does not have a time frame set for reconsideration of its decision.
"The decision was made due to the current unfavourable investment climate."
Stamford Bridge currently has a capacity of 41,631, and if the development plans went ahead then it would have been Europe's most expensive stadium at a cost of £1billion.
