The 24-year-old has not played for Rovers since September due to feeling ill and medical tests have since found the former Rochdale winger has contracted nodular sclerosing Hodgkin's disease.
Thompson will now undergo a six-month course of chemotherapy.
"We are stunned by the news and all our thoughts are with Joe and his family," said chief executive Mick Horton.
"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."
Tranmere boss Ronnie Moore added: "Joe is a fantastic young man and he will be missed around Prenton Park while he has treatment.
"He has the full support of all the coaching staff and his team-mates and we will do everything we can to help him make a full recovery."
Thompson joined Rovers in 2012 and has made eight appearances this season, scoring twice in a 3-3 draw against Crawley in August.
- Disease & Medical Conditions