Members of the Rail, Maritime and Transport union at Euston and Green Park will walk out on Friday 3 June.
General secretary Mick Lynch said those based at the two stations had “suffered years of sustained bullying and intimidation by a manager”.
Transport for London (TfL) urged the union “not to take strike action”.
The strike is on the same day as a service of thanksgiving being held at St Paul’s Cathedral to commemorate the Queen’s 70-year reign.
The Northern and Victoria lines both run through Euston station, while Green Park is served by the Victoria, Piccadilly and Jubilee lines.
The Northern and Victoria lines both run through Euston station
While staff at only two stations are due to take action, Mr Lynch said the strike would “cause significant disruption to people wishing to celebrate the Queen’s Jubilee”.
“However, if Tube bosses do the right thing, and deal appropriately with the manager in question, we can find a just resolution to this dispute,” he added.
A TfL spokesperson said: “We hold our people to high standards and ensure everyone is treated fairly.
“We’re aware of this dispute and are carrying out an urgent review in a bid to resolve it.”
The transport body has advised that if the action does go ahead there should be no effect on train services, although “we are reviewing what the likely impact will be at those stations”.