The note, found by Florence Widdicombe, was allegedly written by prisoners in Shanghai claiming they were "forced to work against our will".
"Please help us and notify human rights organisation," the message said.
Tesco said it was "shocked" by the report, adding: "We would never allow prison labour in our supply chain."
The supermarket said it would de-list the supplier of the cards, Zheijiang Yunguang Printing, if it was found to have used prison labour.
Florence was writing cards to her school friends when she found that one of them - featuring a kitten with a Santa hat - had already been written in.
In block capitals, it said: "We are foreign prisoners in Shanghai Qingpu prison China. Forced to work against our will. Please help us and notify human rights organisation."
It asked whoever found the message to contact Peter Humphrey, a British journalist who was himself imprisoned there four years ago.