Vicky Pryce, 60, will stand trial again for perverting the course of justice as early as next week after the jury at Southwark Crown Court was discharged.
The jury had said it was highly unlikely it would reach even a majority verdict.
Mr Justice Sweeney said he had never seen a situation like it in 30 years after being presented with a list of 10 questions by the jury yesterday, following nearly 14 hours of deliberations.
They included: "Can a juror come to a verdict based on a reason that was not presented in court and has no facts or evidence to support it, either from the prosecution or defence?"
The judge said: "Quite apart from my concern as to the absolutely fundamental deficits in understanding which the questions demonstrate I wonder ... the extent to which anything said by me is going to be capable of getting them back on track.
"In well over 30 years of criminal trial I have never come across this at this stage, never."
Prosecutor Andrew Edis, QC, said the jury of eight women and four men did not appear to have truly understood its task.
He said: "I don't ever recollect getting to this stage in any trial, even in more complicated trials than this one, and after two days of deliberations a list of questions of this basic kind illustrating that at least some jurors do not seem to have grasped it.
"This is not a classic case of jury irregularity or misconduct. This is a fairly unique situation where, after a short and legally simple case, a jury has after a long retirement sent out a note containing nine questions which are aimed at attempting to understand the fundamental purpose of their presence."
Mr Justice Sweeney gave the jury lengthy directions in a bid to answer their questions, but less than two hours later they said it was highly unlikely they would reach a verdict.
Pryce, 60, of Clapham, south London, now faces a retrial, possibly as early as next week.
Huhne, who changed his plea to guilty on the first day of a joint trial with Pryce, will not be sentenced until the retrial is complete, the court heard.
During the trial at Southwark Crown Court Pryce claimed a defence of marital coercion, claiming Huhne forced her to take speeding points for him nearly a decade ago, in 2003.
He had been caught speeding on his way back from Stansted airport and thought he would lose his licence, threatening his chances of being nominated to run as the LibDem candidate for Eastleigh, Hampshire.
He went on to win the seat, despite being banned from driving that year for another offence.
The points-swapping allegation became public in 2011 when it was published in two newspapers, nearly a year after the former Cabinet minister confessed to an affair with PR adviser Carina Trimingham, ending his 26-year marriage.
During the trial, it emerged Pryce, once a top economist for the Government, spent months trying to reveal the scandal to the press so she could "nail" Huhne, 58, after he left her for Ms Trimingham in June 2010.
The story was published in two newspapers in 2011, sparking a police probe, and Huhne and Pryce were charged last year.
Huhne, then energy secretary, stepped down from the Cabinet vowing to fight the charges.
His attempts to get his case thrown out failed and he changed his plea on the first day of the trial, ending his political career.
During Pryce's trial, the mother-of-five said he demanded she have an abortion in 1990 as it would be bad for his career, and tried it again two years later, but she resisted.
A summary of some of the questions the jury in the Vicky Pryce trial asked Mr Justice Sweeney.
Please expand upon the definition of marital coercion, does this defence require violence or physical threats?
Judge: It did not require violence or physical threats and meant a woman was so affected by pressure from her spouse that she was "impelled" to commit an offence.
What should the verdict be if the defendant was guilty, but there is not enough evidence she signed the penalty notice to be sure beyond reasonable doubt.
Judge: You can convict only if at least 10 were sure Ms Pryce was guilty, but if you can't agree, you must get the foreman to send me a note to that affect.
If there is debatable evidence supporting the prosecution's case, can inferences be drawn to arrive at a verdict by inferences or speculation about the full evidence
Judge: No. The drawing of inferences is permissable - speculation is not.
Define reasonable doubt.
Judge: A doubt which is reasonable. These are ordinary English words that the law doesn't allow me to help you with beyond the written directions that I have already given.
Can a juror come to a verdict based on a reason that was not presented in court and has no facts or evidence to support it either from the prosecution or defence?
Judge: Said no, again saying while they could draw inferences, they could not speculate.