Members of the Public and Commercial Services (PCS) union are taking action at sites across Wales in protest over plans to stop extra payments to weekend and bank holiday staff.
Industrial action starts at Big Pit in Blaenavon, Torfaen.
National Museum Wales said it faced a 4.7% cut in Welsh Government grant aid and could not continue payments in their current form.
Wales secretary of the PCS, Shavanah Taj, said: "The dispute has dragged on for two years and morale is at rock bottom.
"We understand that the museum's budget has been cut but don't accept it should be the front of house staff, the poorest paid in the organisation, who should make the greatest sacrifice, by giving up their weekend pay."
On Tuesday, National Museum Wales said the union had backtracked on an agreement to ballot members over a proposed resolution.
A museum spokesman added: "Resolving this dispute is now a matter of urgency, due to the pressures of a reduced budget. Therefore, it has no choice but to proceed to individual consultation."
The first in a series of strikes over the Easter weekend begins on Friday.