Members of the Transport Salaried Staffs' Association (TSSA) said its members had been subjected to increased threats and abuse since a programme of ticket office closures started.
The result of the vote is due at the end of November threatening strikes in the run up to Christmas.
An LU spokesman said it does tolerate any form of assault on its staff.
A survey for the TSSA said most of the 540 staff felt less safe since they moved from ticket offices on to station concourses.
The union said staff were being targeted by frustrated passengers if ticket machines do not work.
The ticket officers were closed as part of the Fit for the Future programme introduced by former London mayor Boris Johnson.
His successor Sadiq Khan has ordered a review of the project.
TSSA leader Manuel Cortes said: "My members say Fit for the Future working practices are fit for nothing and should be scrapped.
"They are overstretched by the rosters, stressed by how unsafe the Tube has become and fed up with the spikes in abuse, both verbal and physical, from passengers."
LU's Steve Griffiths said: "Everyone has the right to go about their work without fear or intimidation and we do not tolerate any form of verbal or physical assault on our staff.
"Our campaign against workplace violence sends a clear message that any assault on staff will be fully investigated and we work closely with the British Transport Police to bring perpetrators to justice."
The first ticket offices closed in February 2015 and Transport for London said the plan would save Â£50m annually.
Hundreds of London Underground (LU) workers are to be balloted over strike action in a row about safety.