One doesn't normally speak of "rights" in discussions of minimum wage. Instead it is an obligation on the company to pay, not a right of the worker. The worker cannot waive the right, since that would mean breaking the law.
If there is an obligation created by law then an individual may be unable to release someone from that obligation.
Other rights and obligations are written in such a way that they may be waived. For example "No soldier...shall be quartered...without the consent of the owner..." The ability of a person to waive their right not to quarter soldiers is explict.
So certain rights can be waived because of the precise wording of the laws that create those right. The question of whether a rational person could ever want to waive a right is central to whether a right can be waived.
A person may rationally choose to represent themselves. A person may rationally choose to quarter a soldier in their house. A person may rationally choose not to own a gun. Thus the rights to a lawyer, fifth amendment rights and the second amendment rights can rationally be waived.
On the other hand a person would not rationally accept less money for work than is offered. No rational person would submit to cruel or unusual punishment, thus one cannot choose to waive these rights