The jury was discharged, ending the trial, The Daily Telegraph reported. Vicky Pryce, 60, is scheduled to return to Southwark Crown Court on Monday for another trial with a different jury.
Pryce and Huhne were charged with conspiring to pervert the course of justice, but he pleaded guilty earlier this month. The charges stem from an incident in 2003 when Pryce allegedly took speeding points for her then-husband to keep him from losing his license.
In 2011, Pryce described her actions in an interview with The Sunday Times. She told the newspaper she wanted to "nail" Huhne, who had ended their marriage after getting involved with another woman.
At her trial, Pryce said she was a victim of "marital coercion."
The jury spent 15 hours in deliberations, beginning last week. On Tuesday, they sent the judge a list of 10 questions, including some Andrew Edis, the prosecuting lawyer, said showed a lack of understanding of how a trial by jury works.
Huhne, who was warned he is likely to receive prison time, will not be sentenced until a verdict is reached on his ex-wife. He resigned from Parliament when he entered his guilty plea.
The criminal charge was a comedown for the former energy secretary. Huhne went from contending for the leadership of the Liberal Democrats in 2007 becoming the first Cabinet minister to resign because of a criminal prosecution five years later.