The group blamed the move on "weak profitability" in the carton sector, and a 90-day period of consultation with Amicus GPM sector has started at the site. The Crown Point factory dates back to 1895.
Around 107 jobs are at risk with the plant employing a total of 213 people. Approximately 106 new positions are to be created at MY Cartons' other Leeds site in Cockburn Fields.
"We are reviewing our Leeds operations to ensure the long term viability of our carton business in the city," said MY Cartons divisional managing director Stuart Goode. "This has led to the board reviewing the two current operations and proposing the closure of the older site."
Goode added that the aim of the consultation had the "overriding aim of avoiding any further redundancies".
"The proposal and consultation process will hopefully secure the future for the business and remaining 560 employees in Leeds," said Goode.
The consultation process will also look into alternative employment elsewhere in the MY Group.
At the start of the year MY Cartons invested 10m to enhance the Cockburn Fields plant. Equipment installed included two additional MAN Roland 906 presses and a second Creo Trendsetter CTP line.
Story by Philip Chadwick