The crash, which also claimed the life of the pilot, occurred when passengers were on an independent excursion from Royal Princess, which was on an Alaskan voyage.
The aircraft are thought to have collided in mid-air in the George Inlet area. All the fatalities were on an unnamed carrier.
The other aircraft involved was operating a Misty Fjords ship excursion and carrying 10 passengers. All were rescued, although Princess Cruises said the condition of one guest was “unknown”.
This aircraft was operated by Taquan Air and, last summer, 11 people survived when one of its fleet crashed into a mountainside. Investigators found that a terrain warning system had been switched off.
In a statement, Princess Cruises said: “It has been confirmed there are five fatalities from the independent air tour – four Royal Princess guests and one pilot.
"Princess Cruises has activated members of its Care Team to provide assistance to the families impacted by today’s accident.”
It added: “We are deeply saddened to report this news and our thoughts are with those who lost their lives and the families of those impacted by today’s accident. Princess Cruises is extending its full support to traveling companions of the guests involved.”
Royal Princess is sailing a seven-day Voyage of the Glaciers cruise that departed Vancouver on Saturday. It will arrive in Anchorage on Saturday 18 May.