The 44-year-old male pilot, who works for Skytrek Hang Gliding and Paragliding, was admitted to Lakes District Hospital with moderate back injuries.
His female passenger, aged in her 30s, received minor injuries in the crash, which occurred in fine weather about 11am.
CAA spokeswoman Philippa Lagan said it had received "good video footage" of the crash and did not plan to send an investigator.
It had not interviewed the pilot, but would consider doing so next week if any questions remained after receiving his written account of the incident.
Ms Lagan said the investigation could take up to three months.
The pair hit a tussock-covered hillside about halfway between their launch site on Coronet Peak and the intended landing zone at Flight Park Queenstown, on Malaghans Rd.
A helicopter with a long line suspended underneath was used to airlift them, in stretchers, from the crash site.
In a media statement, Skytrek said its pilot was kept in hospital for observation overnight on Thursday, while the passenger was treated and discharged the same day.
A spokeswoman for the company could not provide an update on the man’s condition yesterday but said it had resumed flying.