The union announced it was holding a ballot over the issue last month, as did train drivers' union Aslef. The result of Aslef's ballot will be announced on Thursday.
Both unions have been protesting what they see as obstruction of drivers' career progression.
RMT general secretary Mick Cash said:
It is outrageous that London Underground have decided to discriminate against their Night Tube drivers.
"This is a senseless and damaging policy that picks out one group of staff for negative treatment and of course the drivers are angry and that is why our members have voted overwhelmingly for action.
"That ballot result will now be considered by RMT’s executive," he added.
According to the RMT, Night Tube train operators "have been prevented from moving into vacant full-time positions for a period of at least 18 months".
The union said all other staff, including part-time Night Tube station staff, are eligible to apply, "but Night Tube train operators are not".
Peter McNaught, operations director for London Underground, said:
Night Tube services have been running since August last year in line with agreements reached with the unions. We’ve met with the RMT to discuss and resolve the new issues that they have.
We have invited the RMT to more talks later this week and I encourage them to continue discussions with us rather than threaten industrial action.
To date, the Night Tube services, which are up and running on five lines, have been more popular than anticipated.
In November last year, London Underground's managing director Mark Wild said passenger numbers were 50 per cent higher than forecast.
The services were first launched on the Victoria and Central Lines on 19 August and then joined by the Jubilee on 7 October. The Night Tube then came to the Northern and Piccadilly Lines.
A separate dispute over a breakdown in industrial relations has seen Tube fleet members undertake a work-to-rule since 7 March. TfL said it wasn't expecting much disruption to services from that action though.