I copied this information from another message board. I don't know exactly how correct it is. The best thing way to find out the minimum age on Princess (or any cruise line for that matter) would be to call either a travel agent, or the cruise line directly.
Cruiseline age requirements :
All cruise lines require that at least one person in each cabin meets a minimum age requirement. The information that follows was provided by the cruise lines at the time of this writing, is subject to change, and should be verified with your Vacations To Go cruise counselor prior to booking.
The lowest minimum age requirement for any cruise line is 18. The following cruise lines require that at least one person in each cabin is 18 or older: Clipper, Cruise West, Cunard, Oceania, Orient Lines, Peter Deilmann, Radisson Seven Seas Cruises, SeaDream, Star Clippers, Uniworld, and Windjammer.
The following cruise lines require that either 1) All passengers in a cabin must be 18 or older, or 2) If anyone in the cabin is younger than 18 years old, someone in the cabin must be 21 or older: Clipper, Disney Cruise Line, Princess Cruises, Silversea and Viking River Cruises.
The following cruise lines require that at least one person in each cabin is 21 or older: Costa (25 for March and April sailings), Crystal Cruises, Delta Queen Steamboat Company, First European Cruises, MSC Italian Cruises, Norwegian Cruise Line, and Seabourn Cruise Line.
The following cruise lines require that either 1) All passengers in a cabin must be 21 or older, or 2) If anyone in the cabin is younger than 21 years old, someone in the cabin must be 25 or older: Carnival, Royal Caribbean, Holland America, and Windstar Cruises.
One cruise line, Celebrity Cruises, always requires that someone in every cabin must be at least 25 years old. Costa has this requirement for their March and April sailings only.
One exception to these age requirements is made for underage married couples, who as long as they are both 18 are allowed to board unaccompanied. These couples may be asked to show proof of their marriage.
Your age on the date of sailing is generally considered your age for the length of the cruise.
Consumption of Alcohol
Once you've left port, the minimum age for the consumption of alcohol varies by cruise line.
First European, Oceania and Radisson Seven Seas allow all passengers 18 and older to consume any type of alcoholic beverage they choose.
Celebrity and Royal Caribbean offer beer and wine to passengers over 18, and all types of alcohol to passengers 21 or older.
Carnival, Clipper, Costa, Cruise West, Crystal, Cunard, Delta Queen, Disney, Holland America, MSC Italian Cruises, Norwegian, Orient, Peter Deilmann, Princess, Seabourn, SeaDream, Silversea, Star Clippers, Uniworld, Viking River Cruises, Windjammer and Windstar require passengers to be at least 21 to consume any type of alcohol.
Gambling, a popular form of entertainment on cruise ships, also has age restrictions which differ between cruise lines. Carnival, Celebrity, Holland America, Oceania, Orient, Radisson Seven Seas, Royal Caribbean and SeaDream require passengers to be 18 or older to play in the shipboard casinos. Crystal, Cunard, First European, MSC Italian Cruises, Norwegian, Princess, Seabourn, Silversea and Windstar restrict the casinos to travelers 21 and older. Costa requires those gambling in the casinos to be 25 or older.