No, although many employers continue to present this as a written or unspoken rule. Employers generally do not want you to share your salary, hourly wage, or bonus numbers with your colleagues because they fear those who make less will demand more pay. However, the National Labor Relations Act specifically protects your right to discuss terms and conditions of your employment, such as pay, with your co-workers. You cannot be disciplined for discussing it. Your employer cannot even make a rule or threaten to discipline you for it.
However, it is important to make something clear about this. If you are discussing your pay with co-workers in a way that violates some other legitimate disciplinary rule at work you may be disciplined for that other reason even though you were invoking your rights under the National Labor Relations Act. For example, if you are having the conversation during working hours while you are supposed to be doing something else, you likely could be disciplined for insubordination or poor work performance for not doing your work. On the other hand, if employees commonly stand around talking while they are on the clock, especially if there is down time where no work is available, an employer cannot chose to only discipline people talking about their pay and not people talking about their weekend plans or their kids. Similarly, if your employer disciplined you and somebody for talking about their kids, they cannot discipline you more harshly than the other person without some other legitimate reason, such as it is your third write up for poor performance.
If you believe your employer has improperly disciplined you for discussing working conditions or pay with your co-workers you should contact my office to discuss your situation.