The crash took place on the Ballymacombs Road, Magherafelt, just after 9.40pm on Sunday.
The driver of the car, a 54-year-old woman, was arrested and was found to be almost four times over the drink-driving limit.
She was arrested on suspicion of driving with excess alcohol and remains in policy custody.
A PSNI spokesperson said the driver was lucky not to be badly hurt.
“Yet again we find ourselves picking up the pieces after another selfish drunk got behind the wheel and drove,” the spokesperson wrote on the PSNI Magherafelt Facebook page.
“How we aren’t picking up the pieces of a broken family or families is simply a miracle.
“As if this wasn’t bad enough the driver then left the scene with the assistance of others in the hope they wouldn’t get caught. A nearby crew tracked their movements and arrested the driver some distance away from the scene.”
The spokesperson said drink driving puts lives at risk.
“It’s pathetic that we have to continually post about drink drivers in this district,” the spokesperson said.
“If you drink and drive we will catch you. Our focus is catching you before you become a killer.
“If you are in any doubt that you’ll be caught pay a visit to Magherafelt Court on any sitting and you’ll see for yourself how relentless we are at catching these individuals.”