Members of the Public and Commercial Services (PCS) union working at venues including the National Museum of Scotland are threatening the walkout in a dispute over weekend working. The Easter strike comes after similar action taken on Boxing Day last year.
If it goes ahead, the museums will be closed for the afternoon.
National Museums Scotland, which also runs the National War Museum, the National Museum of Flight and the National Museum of Rural Life, said in a statement: "We have been given notice of possible strike action on the afternoon of Friday 11 April across National Museums Scotland sites.
"In view of this being the Easter holidays we'd like to give our visitors advance notice of this anticipated action and thereby avoid disappointment. These circumstances are entirely outside our control and we apologise for the inconvenience caused to visitors."
The museums will be open as normal on Saturday.
The PCS says its members are "suffering a huge detrimental impact on their standard of living" as a result of the decision to scrap weekend working payments to staff hired from 2011 onwards. The allowance is normally paid to compensate staff for working anti-social hours, but the decision to axe the payment has resulted in a split in the workforce between those who are still paid extra and those who have never received the allowance.
Lynn Henderson, PCS Scottish Secretary, said: "Museums staff will not tolerate the two-tier workforce. Such shameful anti-worker policies should be left in the past or at best be an artefact on display in the museum."