"He's pretty much got two collapsed lungs, a fractured sternum, and fractured ribs," she said.
The sister was unaware of how her brother was injured in the incident but said he worked as a drainlayer.
Police and Fire and Emergency New Zealand also attended the incident where firefighters worked to get oxygen and a stretcher into the trench.
Footage captured at the scene shows several firefighters and ambulance staff working at the scene and assisting the trapped worker.
Firefighters rescued the worker from the trench on a stretcher before the person was placed in an ambulance.
Tse said other person was transported to the Auckland Hospital emergency department in a critical condition.