No, but depending on the state law that applies, there may be some restrictions and added qualifications about who can serve and how they operate.
Legally, a person is free
to choose anyone he or she wants to act as executor. In most states, the only people who can't serve as executors are children under 18 or convicted felons.
However, some states do impose restrictions on out-of-state executors. For example, a few require that an out-of-state executor must be a relative or a primary beneficiary under the will. And some state laws specify that a nonresident executor must obtain a bond or name an in-state resident to act as the estate's representative before he or she can act.
To do a quick check of the law that applies, do an Internet search of the name of the state in which the estate is located, plus “law” plus “executor.” You should be able to pull up the proper probate law that way and find out whether the state imposes any specific restrictions.