There is no minimum age as long as you meet the very strict social security definition of disability .  But to qualify for disability benefits you must have worked long and recently enough under Social Security to earn the required number of work credits.  You can earn up to a maximum of four work credits each year.  The amount of earnings required for a credit increases each year as general wage levels rise. 

The number of work credits you need for disability benefits depends on your age when you become disabled.
Go to http://www.socialsecurity.gov/dibplan/dqualify3.htm to see how many credits you may need to qualify for disability benefits.