The owner of the rental property I manage wants to limit the number of people who can live in the property. Will such a policy violate fair-housing laws?

Possibly. A property owner who tries to impose limits on families with children may be violating fair-housing laws that protect familial status. 

The U.S. Department of Housing and Urban Development says an occupancy policy of two people per bedroom can be reasonable, but other factors should be considered, including the size and number of bedrooms, the age of the children, and the configuration of the unit.

You should ensure that your occupancy policy is consistent and applies to all occupants and rental applicants. For example, you can’t refuse to rent to one family because they have children or demand that a tenant with a baby on the way move to a larger unit.

What does "familial status", one of the protected classes under the federal Fair Housing Act, include?

"Familial Status" is defined as any family in which one or more individuals (who have not attained the age of 18 years) live with a parent, a legal custodian, or a designee of the parent or legal custodian, with the written permission of the parent or legal custodian.The protections against discrimination also apply to any person who is pregnant or is in the process of securing legal custody of an individual who has not attained 18 years.