No-one was injured but Australian tourists aboard said some people were knocked off their feet by the impact.
Two other vessels towed the damaged boat back to its berth on Wednesday.
Mitre Peak Cruises is a subsidiary of Queenstown tourism giant Skyline Enterprises.
Skyline chief executive Jeff Staniland said from looking at the damage "it's been a solid hit''.
"The gearbox failed and they couldn't do anything, so they kept going and hit the rocks.
"It wasn't holed.
"There was damage to the hull, which is just really a big dent. That's getting repaired.''
He hoped the boat would be operating again by the middle of next week.
"It's quite a busy time of the year, of course, so it could well be that we won't be able to accommodate everyone.''
The damaged vessel is Mitre Peak 1, the smaller of the operation's two boats.
It was towed to its berth by Mitre Peak 2 and a Jucy tourist boat.
Mr Staniland did not know where on Milford Sound the accident happened.
The company had advised maritime authorities of the incident.
The Christchurch companies behind a proposed Fiordland tunnel bought Mitre Peak Cruises from Neil Sutherland, of Dunedin, in 2006.
Two years later it was bought by the Totally Tourism group of companies, which was swallowed by Skyline in 2011.
