The west London club had been expected to press on with the construction of its new 60,000 seat stadium after a series of hold ups, with a completion date set for the start of the 2023/24 season.
But in a dramatic move, the Russian billionaire has put the plans on ice after he was caught up in a visa crackdown by the UK authorities in the wake of the Sergei Skripal nerve agent attack in Salisbury.
The club cited “unfavourable investment conditions” as the reason for the decision.
The Government is conducting a review on all foreign investor visas amid increasing diplomatic tensions between Westminster and Moscow.
His decision to call a halt to the stadium plans could be viewed as a major powerplay by the Russian in response to the Home Office hold-ups and may trigger similar moves by other oligarchs waiting on their tier one visa decisions.
Mr Abramovich is expected to move to Tel Aviv, having secured Israeli citizenship earlier this week, which provides the oil magnate access to the UK without a visa for up to six months.
But Downing Street confirmed on Tuesday the oligarch, who is worth £9.3bn and ranked 13th on the Sunday Times Rich List, is not allowed to work as an Israeli without a visa.
Reports emerged the businessman has since withdrawn his investor visa application with the UK until the Government has completed its review.
The Jerusalem Post reported Mr Abramovich pulled his application after he gained Israeli citizenship as he was willing to wait for the UK to set a new policy.
Mr Abramovich has owned Chelsea since 2003 and the club was expected to start work on the new stadium to increase its capacity from 41,000 to 60,000 at the end of the 2019/20 season.
Officials were looking into moving home matches to Wembley for as much as four years while the building work was taking place, although the potential change in ownership had complicated the plans.
In a statement, the football club said: “Chelsea 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.”