The decision by the military-backed, civilian-led government - the latest in a series of reforms since last year - reduces the list by about a third.
No other details of who had been taken off the list were provided.
The move came a day after the president announced a major cabinet reshuffle.
The reshuffle is the largest since President Thein Sein's government took office in March 2011, after the military junta ceded power.
"These relaxations are in line with the country's transformation," presidential spokesman, Nay Zin Latt, was quoted by the Associated Press news agency as saying.
He added that more names would be eventually removed, and "only those who were put on the blacklist due to criminal and other economic misdemeanors will remain on the blacklist".
State media said the removal of names from the list gave a green light to Burmese citizens abroad to return home.
"In the past, companies and persons from all fields including media men were blacklisted and banned by the government in the national interest," reports the state-run New Light of Myanmar newspaper.
"But the government is lifting the ban on them in accord with the reforming system."
The blacklist - which the newspaper said included a total of 6,165 names - has also been known to include government critics, foreign journalists and public sector workers who went abroad during military rule.
Actress Michelle Yeoh, who played Burma pro-democracy leader Aung San Suu Kyi in the film The Lady, was among those previously blacklisted.
Author Benedict Rogers, who wrote the biography of former military leader Than Shwe, was also included several times.
During nearly five decades of military rule thousands of people - foreigners and Burmese - were blacklisted by the authorities. Some were expelled, others living overseas, especially political activists, assumed they could not return, or that they would be arrested if they did.
Since the new government's reforms, some Burmese living overseas have tested the restrictions and been allowed to return. Observers say a measure of the extent of the reforms will be whether prominent exiled activists are allowed back into the country.
Burma has announced the removal of 2,082 names from its blacklist, which bars people deemed a threat to national security from entering or leaving the country.