Members of Morocco's parliamentary committee on foreign affairs, national defence and Islamic affairs are also expected to stage protests at the Spanish embassy in Rabat.
The Moroccan authorities were angered last week when the Spanish government announced that the king would be visiting the enclaves, located on Morocco's northern coast.
The Moroccan government has said the planned visit is "regrettable" and recalled its ambassador to Spain in protest.
Madrid has sought to soothe the tensions.
Miguel Morantinos, Spain's foreign minister, said: "We hope that the good level of relations between Spain and Morocco will allow us to get over the sensitive points of this issue".
Morocco believes that Spain "occupies" both Ceuta and Melilla and regards both as part of Moroccan territory.
Spain says the cities, which are remnants of their colonial empire, have been Spanish for more than 400 years, longer than Morocco has been a sovereign state.
Security measures have been increased in the area, with around 700 extra Spanish officers implemented to guard the royals.
The row has not dampened the enthusiasm of residents in the area.
Authorities began distributing tens of thousands of Spanish flags to residents of both cities on Sunday.
"I am Muslim but I have thought for a long time that he should come. I am happy to see him", Driss Mohammed, a local resident, said.
The king is set to visit the Melilia parliament on Tuesday.
It is the monarch's first visit to the area in 32 years as head of state.