Kenneth Petty was required to inform authorities when he moved due to an attempted rape conviction in 1995.
But the 44-year-old admitted failing to do this when he relocated to California with Nicki Minaj in 2019.
He’s now been sentenced and fined $55,000 (£46,000), according to the US Attorney’s Office.
Under US law, registered sex offenders have five days to update their details if their residence changes.
Petty had previously pleaded not guilty to this at a 2020 court appearance but changed his plea last September.
At his latest hearing, prosecutors said house arrest was not tough enough, and urged the judge to give Petty further prison time.
In the hours after the sentencing, Nicki Minaj posted a picture on Instagram of her husband and son.
Petty began dating the rapper in late 2018, with the pair having reportedly known each other since childhood.
A year later they were married and they now have a son.
Their relationship has proved controversial due to his criminal past, with Nicki defending her partner against criticism.
In August 2021, the pair were sued by the woman he was convicted of attempting to rape.
She filed a lawsuit alleging that the couple harassed her to try to make her take back her claims.