The 30-year-old, who plays for Norwegian club side Rosenborg, has appealed the sentence, his lawyer said.
The Denmark star, who was arrested in September after being reported to police by the driver, was earlier pictured arriving with lawyer Anders Nemeth for his trial.
Bendtner broke the taxi driver's jaw in September after a night out in Copenhagen and the court was shown a video from inside the cab of the incident.
Having refused to pay the £4.80 fare, the forward – who earned £50,000 a week at Arsenal – punched the driver before kicking him as he lay on the ground.
He has also been ordered to pay the cabbie more than £1,000 in compensation.
In surveillance video of the incident in September, Bendtner appears to strike the driver in the face and kick him after a row started over which way the driver was supposed to drive.
Bendtner admitted to hitting the taxi driver in the face.
But he said it was because he felt threatened when the driver threw a bottle or a can towards him and his girlfriend when they left without paying.
The cab driver, whose jaw was broken, was acquitted of violence but fined £350 for using his telephone while driving and not wearing his seatbelt.
Reflecting on the incident Bendtner said: “I was involved in an extremely unfortunate episode.
“I could not imagine it would develop as it did, and of course I’m extremely sad that the outcome became as unfortunate as it did.
“To Rosenborg fans and audiences, I regret that this has happened. I’m sorry with all my heart that we are standing here today.
“To my dear teammates, I regret that this will steal focus in an important time. I thank you for your understanding.
“I have never been a fighter but I protect those I love on and off the pitch.”
The jail sentence is another chapter in a colourful career for the former Premier League player.
Bendtner started his pro career at Arsenal, scoring his first goal for the club when still a teenager.
But despite much promise, Bendtner failed to ever live up to the hype (which was often generated by himself).
His best season came in 2008/09 when he netted 14 goals in 50 appearances for the club.
After loan spells with Birmingham, Sunderland and Juventus, Bendtner left the Emirates in the summer of 2014 to join German side Wolfsburg.
After two disappointing years he returned to England with Nottingham Forest before joining current club Rosenborg a year later.
Bendtner landed himself in hot water Euro 2012 after he celebrated a goal by pulling his shorts down to reveal boxer shorts sponsored by a betting firm.
He was also bought a plot of land in Scotland which comes with a title – leading to his nickname "Lord Bendtner". He later became known as the"emperor".
As reported, in March 2014 he allegedly unbutton his pants, rubbed his privates on a taxi and then while whipping a taxi and then called the driver a “little bitch” and a “fat little pig”.
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