A row has erupted after 430 Tesco sales assistants claimed they have been asked to do the cleaning.
Staff at the supermarket giant's 26 Express stores said their managers instructed them to carry out duties that used to be done by a contract cleaning company.
The staff, who normally man the checkouts, said they were asked to tidy up and carry out work that included operating industrial cleaning machines.
When they objected, they said managers told them they should continue to carry out the cleaning although it had not been agreed with their union.
Mandate has written to the company, saying the cleaning work was "not appropriate" for sales assistants. It said it had concerns in relation to their health and safety.
It said Tesco's decision to end its relationship with the contractor and assume staff would "naturally perform" the cleaning was in breach of their employment contracts and management agreements with the union.
In an internal report to members, Divisional Organiser Brendan O'Hanlon said the supermarket chain failed to warn staff of its plans for the cleaning operations.
He said this was despite the fact that talks took place regularly to discuss issues arising at the stores.
When contacted yesterday, Mandate said it had entered talks with the company over the cleaning dispute at Tesco Express.
"Given that there is a process of discussions under way, the union does not believe it is appropriate to make any further comment," said a spokesman.
Tesco said it was in discussion with the union and would not comment further.
The supermarket chain revealed yesterday that Ireland had delivered its first full-quarter sales growth since 2010, rising by 0.4pc in the first quarter of the year.