The 35-year-old was sent for tests after missing this week's County Championship match against Warwickshire because he felt unwell.
He will have more examinations before receiving treatment.
Hampshire chairman Rod Bransgrove said: "I would like to send him and his family our very best wishes at this very difficult time."
Left-hander Carberry missed an England Performance Programme tour in late 2010 and part of the 2011 season because of blood clots on a lung.
He averaged 28.75 in six Tests for England, the most recent of which was against Australia in 2014.
England batsman Michael Carberry has been diagnosed with a cancerous tumour, his county Hampshire have confirmed.