Bectu says a number of local union officials at the Ritzy, which has several cinemas in London, have been disciplined.
The workers have been campaigning to be paid the voluntary London Living Wage of Â£9.75 per hour.
Picturehouse cinema, which runs the chain and is part of Cineworld, said workers were paid Â£9.65 per hour.
That is based on seven-and-a-half hours worked in an eight hour shift.
The union, now part of Prospect, says the move is "appalling" and strikes are set to be held on Saturday and Sunday.
Bectu leader Gerry Morrissey said: "Bectu members in Picturehouse have been striking for over 10 months for a Living Wage, company sick pay, and union recognition.
"It is appalling that Picturehouse and Cineworld would rather intimidate and threaten to dismiss their staff than enter constructive negotiations.
"This is clearly an attempt to break the union by undermining the strike and intimidating other workers."
Picturehouse said: "This is an internal matter - we are investigating possible unlawful activities and we cannot comment further at this stage."
On its website, it says workers do receive sick pay and four weeks' holiday a year.
Three years ago, staff held 13 strikes over their pay and the minimum wage was raised.
Leaders of cinema workers involved in a long-running dispute over pay say they have been suspended ahead of talks.