The Dubai-based Arabic station said on Sunday that the threats accompanied criticism of the channel in the Syrian state-run daily Tishrin.
"Al-Arabiya expresses its extreme concern over Tishrin newspaper's method in accusing the television of treachery. This was accompanied with threats directed against a number of our colleagues in Beirut," the television said in a statement faxed to the media.
A source at the station, referring to Syrian security, said: "There were death threats against Arabiya's staff in Beirut by the Syrians."
Syrian officials were not immediately available to comment.
Al-Arabiya said it had aired the interview with Annan in full and without interpretation or exaggeration.
"This incident, along with many other incidents, raises dozens of questions about the mission of this station and the bodies that run and finance it"
Syrian state-run daily Tishrin
In it, UN Secretary-General Annan urged Syria to withdraw its troops from Lebanon by April, when he is due to present a report on the situation to the Security Council.
In a front-page article on Saturday, Tishrin accused Al-Arabiya of ignoring later remarks by a UN spokesman who said Annan had not been setting a deadline.
"This incident, along with many other incidents, raises dozens of questions about the mission of this station and the bodies that run and finance it," Tishrin said about the majority Saudi-owned station, which is seen by some Arabs as pro-Western.
Al-Arabiya said the newspaper's criticism was unjustified.
"Al-Arabiya has aired interviews with Syrian officials and analysts to answer the secretary-general ... as it was keen to give a balanced report," the statement added.
Syria said last week that it would pull back more troops to eastern Lebanon in line with a 16-year-old agreement that ended Lebanon's civil war and that it was ready to work with the United Nations to implement a resolution calling for the removal of Syrian troops.
International pressure for Syria to quit Lebanon has grown since a bomb killed former Lebanese prime minister Rafiq al-Hariri last week.
Many Lebanese hold Syria responsible for his death.