The 90-year-old statesman underwent surgery to remove a small mass in his liver earlier this month.
He said he would reveal more "when facts are known, possibly next week".
Mr Carter will undergo treatment by physicians at Emory Healthcare in Atlanta.
President Barack Obama wished Mr Carter "a full and fast recovery" in a statement released on Wednesday.
"Jimmy, you're as resilient as they come, and along with the rest of America, we are rooting for you," Mr Obama said.
The White House said Mr Obama spoke to Mr Carter on the telephone on Wednesday.
Bernice King, daughter of Martin Luther King Jr, posted on Twitter: "President #JimmyCarter is in my thoughts & prayers. May the Lord heal, comfort & encourage this extraordinary servant-leader to the world."
Leaving the White House in 1981, Mr Carter has remained active carrying out humanitarian efforts with his Carter Center in recent years.
He founded the centre, which focuses on human-rights efforts and political mediation, soon after he left office.
He was later responsible for negotiating a 1994 nuclear disarmament pact with North Korea and has visited Syrian President Bashar al-Assad in recent years.
A Democrat from Georgia, Mr Carter was elected president in 1976.
He won the Nobel Peace prize in 2002 for his commitment to finding peaceful solutions to international conflicts, his work with human rights and democracy initiatives and his promotion of economic and social programmes.
The BBC interviewed Mr Carter in February about his efforts to eradicate guinea worm disease and in the South Sudan and Mali and river blindness in both Africa and Latin America.
He said then he was happy to still be travelling and doing work across the globe.
But in May, he returned early from a trip to observe elections in Ghana because he was "not feeling well".
Mr Carter has been recently promoting his latest book, A Full Life: Reflections at Ninety, which was released in July.
Former US President Jimmy Carter says recent liver surgery revealed that he has cancer and it has spread to other parts of his body.