Mr Lungu, elected in January, collapsed while giving a speech to commemorate International Women’s Day in the capital, Lusaka on Sunday.
During the campaign, Mr Lungu’s allies denied reports he was sick and offered to undergo a medical check-up.
The election was called because of the death of his predecessor Michael Sata.
Mr Lungu, 58, was treated at a local hospital and his office issued a report assuring Zambians that the president was “feeling better” and would return home on Monday.
A statement from the president’s office said he was suffering from a narrowing of the oesophagus which needed “high-tech medical procedure which is currently unavailable in Zambia”.
“There he has been referred for specialised treatment abroad,” it said.
It said this was a recurrence of a condition for which he had been treated 30 years ago.
The statement did not specify when Mr Lungu would have the operation and journalists were not allowed to ask questions at the press briefing.
Mr Lungu, a former defence minister, is due to serve the remainder of Mr Sata’s term, until elections in 2016.
While Mr Sata was president, the government was accused of covering up his ill-health.
