Jane Collins, who represents Yorkshire and North Lincolnshire, claimed the MPs knew about child exploitation in the town but did not intervene.
The MPs - Sir Kevin Barron, John Healey and Sarah Champion - sued for libel.
But the High Court was told Ms Collins has applied to the European Parliament for immunity from prosecution.
Mr Justice Warby said on Tuesday he was obliged to grant a "stay" on the proceedings at London's High Court pending the European Parliament's decision.
Ms Collins has been sued for slander and libel by Sir Kevin, MP for Rother Valley, Mr Healey, who represents Wentworth and Dearne, and Ms Champion, MP for Rotherham.
They have complained about a speech she gave at UKIP's conference in September 2014 - a month after a report found that about 1,400 children in the area had been abused between 1997 and 2013.
Lawyers for Ms Collins argued it was a political speech that did not contain any allegation of fact, but expressed an opinion to the effect that the MPs were likely to have known sexual exploitation was a serious problem in the area.
A year ago, Ms Collins made an offer of amends that was accepted.
However, the amount of compensation could not be agreed so the case came back to court this week for the assessment of damages, which the MPs have said should be about Â£150,000 each.
Ms Collins, who is representing herself in court, has now applied to set the agreement aside, claiming she did not give informed consent.
Gavin Millar, QC for the MPs, said: "It is simply an attempt to get out of the bargain she made and yet another example of her inability to accept the consequences of her own actions."
A bid by Rotherham's three Labour MPs to get compensation from a UKIP MEP over remarks she made about the town's child abuse scandal has been suspended.