A police spokeswoman said they received reports of the crash in Eglinton Rd, between McGeorge Ave and Stafford St, in the suburb of Mornington, about 3.15pm.
Police, St John and Fire and Emergency New Zealand attended the scene.
A St John spokeswoman said one ambulance was sent to the crash and two people in the Jeep were treated at the scene.
No other vehicles were involved, she said.
Police said the northbound lane of Eglinton Rd was blocked and traffic control was implemented by the Dunedin City Council.
The power pole could be seen snapped in half and airbags had deployed in the vehicle.
An Aurora Energy spokeswoman said a faults crew was dispatched at 3.30pm.
One customer was affected; their power was restored by 8pm, she said.