Margaret Loughrey, 50, from Bridge Street, Strabane, admitted a number of offences.
She was ordered to pay £559 for damaging the driver's glasses and £200 compensation to the driver.
Ms Loughrey's win was the largest ever jackpot win in Northern Ireland.
As well as assaulting the driver, Ms Loughrey also pleaded guilty to causing criminal to his glasses and SatNav during the incident in his taxi at Chestnut Park in Strabane on 14 May.
Ms Loughrey's solicitor said she had come to court with a clear record and had been drinking vodka with friends all night before the incident.
He described her behaviour as shameful and said it was unfortunate her reputation was now blemished.
The deputy district judge at Strabane Magistrates' Court said he believed it was a "one-off incident" caused by Ms Loughrey consuming a lot of alcohol.
"You have had more advantages than most people in the last number of years, but they have obviously brought some problems," he said.
"I accept you have made a major contribution to the local community, but you will be treated as anyone else will be treated coming before the court with a clear record."
A County Tyrone woman who won £27m in the Euromillions draw in 2013 has been ordered to complete 150 hours of community service after pleading guilty to assaulting a taxi driver.