The 24-year-old will begin a six-month course of chemotherapy treatment after it was revealed that he is suffering from nodular sclerosing Hodgkin's disease.
The midfielder, who began his career at Rochdale, underwent medical tests after complaining of an illness.
Chief executive Mick Horton told the club's official website: "We are stunned by this news and all our thoughts are with Joe and his family. Joe will get all the love and support we can give him as he undergoes his treatment.
"We ask that the privacy of Joe and his family is respected and we will share information with supporters as and when we receive it. I'm sure all of our fans will join us in wishing him a full and quick recovery."
Thompson has made six league starts for Tranmere this season, netting two goals.