Divine Muheto, who won the most recent Miss Rwanda pageant, was also fined 190,000 Rwandan francs ($140; £109).
Ms Muheto last month crashed her car into an electricity pylon and a palm tree while driving home from a bar in the capital Kigali, according to local site the New Times.
At the time, a statement said she had fled the scene, but the court acquitted her of this charge.
She wasn’t present at the court hearing, and neither was the prosecution that had sought two years in prison for her.
After 18 days in police custody, the judge ordered her immediate release.
It is not clear if the prosecution will appeal against the judgment.
Ms Muheto hasn’t publicly reacted to the incident. But her lawyers say she has expressed remorse and asked forgiveness.
This is not the first time the 21-year-old has driven under the influence of alcohol, according to police in the East African country.
She rose to fame in Rwanda after she won the national beauty contest in 2022.
The competition has not been held since – it was suspended by the government after sexual misconduct allegations were made against the organisers.
Drink-driving carries a fine of 150,000 Rwandan francs ($110; £85) and five days in police custody.
Thousands of people have been arrested for this crime in recent years as police have begun to enforce the law.
