The 35-year-old left-hander saw a specialist on Tuesday after missing a championship match against Warwickshire because he had felt unwell.
Hampshire said in a statement that following the diagnosis “further tests would be undertaken before the relevant treatment commences.
“Michael has been part of the Hampshire Cricket family for 10 years and on behalf of everyone at and associated with the club, I would like to send him and his family our very best wishes at this very difficult time,” said chairman Rod Bransgrove.
“‘Carbs’ has taken on and beaten serious illness before and we will be doing all we can to make sure he does the same again this time.”
Carberry has previously suffered from blood clots on the lung, missing the start of the 2011 season.
The batsman played for England at test, one-day and Twenty20 with his last appearance in a one-day series against Sri Lanka in May 2014.