The 30-year-old fly-half pleaded guilty at Jersey Magistrates’ Court to resisting arrest and common assault.
Cipriani was fined after pleading guilty to charges of assault in a bar on Jersey.
Mike Preston, defending, said Cipriani had suffered “extreme embarrassment and knows he has let himself, his family and his club down”.
Cipriani, who has only just returned to the England squad, was arrested in the early hours of Wednesday after arguing with a doorman at the Royal Yacht Hotel in St Helier and grappling with police.
He released a statement, saying: “I want to start with a heartfelt apology.
“To my club, teammates, supporters and most importantly the police.
“They have a tough and vital job and I’m mortified that, earlier this week, I acted in a way that I hugely regret. I am truly sorry.”
He went on to say: “I would also like to put on record the words of the Magistrate Sarah Fitz who publicly stated that ‘it was a minor incident’ and ‘a fine is more than sufficient’.
“I was wrong to argue with a bouncer, and pull on his camera tie. I was also wrong to resist arrest.
“This is why I pleaded guilty to these two charges and all other charges were dropped by the prosecution. I was initially confused as to why I was being arrested by three officers.
“This led me to react in the wrong manner for a matter of seconds, seeking to hold off the police officers rather than accepting their decision.”
Prosecutor Samantha Morris Morris said the incident began when the doorman stopped Cipriani from walking out of the bar with two drinks.
After Cipriani became “physically aggressive”, the doorman called police, she added.
Ms Morris said Cipriani “refused to understand why he was being arrested” and “tensed up”, refusing to put his arms behind his back.
The court heard he had one hand in a handcuff but broke his other arm free, pushed towards the female officer and grabbed hold of her shirt.
The officer suffered sustained bruising to her right bicep and reddening to her chest, Ms Morris told the court.
Mr Preston said Cipriani “is very sorry for his behaviour, which lasted a few seconds”.
After appearing in court on Thursday, Cipriani was fined £1,500 for resisting arrest and £500 for assault.
He was also ordered to pay £250 in compensation to the police officer.
Cipriani also stated: “It goes without saying, given the words of the Magistrate, that I didn’t strike anyone or initiate aggression in any way.
“I was on a team night out with the whole squad. I am grateful to the club, who have been fully supportive.
“I would like to publicly thank the Magistrate and the police and, once again, apologise both to them and to the public.”
In June 2015, Cipriani was convicted of drink-driving after crashing his black Mercedes into a taxi in London.
He started a Test for England for the first time for 10 years against South Africa in Cape Town in June.
Last week, he vowed to do “everything I can” to remain part of the team.
He begins the domestic season with his new club at home to Northampton on 1 September.