Tony Vita, 47, was told he should serve a minimum of 12 years before being eligible for parole after being found guilty of repeatedly stabbing 48-year-old Crown Office manager Marion Vita at their house in Glasgow.
The court heard the attack happened on September 20, 2013, after he discovered she was having a lesbian affair with fraud analyst Elwira Rumniak, 34.
A jury at the High Court in Glasgow rejected his claim that she had died in a bizarre accident after falling on a knife during a struggle.
Now Lord Advocate Frank Mulholland, QC, has lodged an appeal against the sentenced imposed on Vita.
A Crown Office spokesman said: "The Crown Office can lodge an appeal only in cases where the sentence could be considered unduly lenient."
Jailing Vita, temporary judge Sean Murphy, QC, said: "This is an incredibly sad case and has had tragic consequences for everyone who knew her, including you.
"You had lived an exemplary life, but all of that ended when you discovered she was having an affair with another woman."
Passing sentence earlier this month, the judge said the incident was a "truly exceptional case given the unusual circumstances".
After the sentencing, For Our Daughters, which campaigns to end violence against women, criticised the judge's comments, saying it was of "grave concern" that he implied Mrs Vita's actions were "in some way to blame for what happened".
They added: "It is perhaps to be hoped that this 'temporary' judge is not too long on the bench."
During the trial, Vita said he had tried to kill himself after discovering his wife had been having an affair for almost a year.
The trial heard how Miss Rumniak and Mrs Vita first met at a party in October 2012.
The court heard Mrs Vita eventually moved to a job with the Crown Office in Edinburgh to be closer to Miss Rumniak.
This resulted in Mrs Vita staying most of the week at Miss Rumniak's flat in the capital, with her husband and son back home in Bailleston.
Ms Rumniak told the court that the couple wanted to set up home together and had talked of adopting a child.
In his evidence, Vita said he did not realise his wife was injured and that he went upstairs and stabbed himself twice in a failed attempt to end his own life.
Detectives who examined the home after the murder found an entry on a calendar in the kitchen for September 20, 2013 that stated: "Marion cheating lesbian whore."
The court was told Vita had also cut his wife out of family photographs and smashed a mug that said "home is where the heart is".