The new service will begin in August but the Rail, Maritime and Transport union balloted members over staffing and performance-related pay.
The union said 85% backed a walkout with a bigger majority in favour of other industrial action.
London Underground said it had made a "fair and sustainable" offer.
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London Mayor Sadiq Khan said the Central and Victoria lines will run through the night on Fridays and Saturdays starting on 19 August, with the Piccadilly, Jubilee and Northern lines following in the autumn.
The Night Tube was due to start last September but was delayed due to disputes with unions, particularly with staff employed by Tube Lines, part of London Underground.
The RMT agreed a deal for its drivers but said the deal for maintenance staff was "inferior".
General secretary Mick Cash said the unions executive will decide its next move but he called for a resumption of "meaningful talks".
He added: "RMT members have now shown their anger at the way that Tube Lines have attempted to tie in attacks on pensions with the offer on pay and Night Tube.
"There are also major unresolved issues over the Tube Lines staffing arrangements for the Night Tube and over performance-related pay."
The strike ballot result is the first faced by the new mayor since he took over from Boris Johnson earlier this month.
London Underground said: "We have made the same fair and sustainable four-year pay offer for Tube Lines maintenance staff as has been made for staff employed by London Underground.
"Pension arrangements for Tube Lines maintenance staff have been the subject of separate ongoing discussions, and we agree that it's important that these talks resume as soon as possible so the dispute can be resolved."
Maintenance workers on the London Underground have voted in favour of strike action in a dispute over pay linked to the Night Tube service.