Contostavlos's Ferrari collided with a Saab outside Southgate tube station in London on 10 September last year.
The 27-year-old admitted driving over the limit with 54 micrograms of alcohol per 100ml of breath. The legal limit is 35 micrograms.
A charge of dangerous driving was dropped by prosecutors.
The singer was also ordered to pay a £1,000 fine, £85 costs and a victim surcharge of £100.
Contostavlos broke down in tears at Highbury Corner magistrates court as she pleaded guilty.
The court heard the singer had consumed two glasses of wine before the incident involving her Ferrari, which she has since sold.
The crash took place at a roundabout outside the station shortly before midnight and officers were called.
'Sleep-driving'
Tarika Jayaratne, prosecuting, said the star - who had taken possession of the sports car just days before the incident - drove "on the wrong side of the road" and hit the Saab which was carrying two people.
Ms Jayaratne told the court that, during her interview at the police station, Contostavlos said she was "sleep-walking" or "sleep-driving" at the time.
Contostavlos's lawyer, Kirsty Brimelow, said the singer was remorseful about what happened.
She described the incident as a "minor collision" and told the court the people in the other vehicle were able to drive home after it happened.
"She immediately cooperated with police. She immediately told the police that she had drunk alcohol," Ms Brimelow said.
She said the star was "a talented young woman" who was set on launching an acting career, saying: "She has placed everything on hold because of this."
She added a conviction would cause the star "difficulties" in getting work in the US.
But in sentencing, judge Gill Allison told Contostavlos it was a "serious matter" and warranted a driving ban.
Contostavlos was a judge on ITV singing talent show The X Factor from 2011 to 2012.
London hip-hop outfit N-Dubz were formed in 2000 and confirmed their split in 2012. Ms Contostavlos also had some success as a solo artist.
Singer and former X Factor judge Tulisa Contostavlos has been disqualified from driving for 15 months after pleading guilty to drink-driving.