It involves the embedding of a microchip in the passport which contains information about the holder, including photographs and fingerprints.
The passports are to be checked at automatic gates installed in the departure terminal at Rangoon international airport.
The e-passports use technology developed by a Malaysian-based company, Iris Corporation, which is partly owned by the UN envoy to Burma, Razali Ismail.
Mr Razali said that 5,000 e-passports would be issued this week to Burmese diplomats, officials and selected members of the business community as part of a pilot programme.
The company hopes that the passport will eventually be introduced in all East Asian nations.
Concerned
But some groups are said to be worried that the information might be misused by the Burmese military government.
Mr Ismail dismissed such fears as unfounded, saying Burma's leaders had changed.
"If you're talking about 10 years ago that may be valid," he told the BBC.
"Must you think of things in such sinister terms? Anyway, it's only for those people who want to travel outside. In most cases those will be government people."
Conflict of interest
Mr Razali also rejected suggestions that his position as UN envoy may have helped Iris seal its deal with the Burmese government.
"There is no conflict of interest," he said. "I've never spoken about this to leaders in government."
Iris' passport concept and interests in Burma predated Mr Razali's assignment as special envoy, he added.
"I have never had to promote it at in any sense at all. I don't know how any watchdogs of right and wrong should pass any judgement on this."