The opposition-controlled parliament voted on 12 March to impeach Roh for breaking an election law by making remarks supporting the minority Uri party and for corruption involving his aides.
Prime Minister Goh Kun is serving as interim leader.
"The recent political situation, unprecedented in the history of our constitution, could add to difficulties facing the economy, which has just started showing signs of a recovery," Finance Minister Lee Hun-jai said in a speech on Thursday.
South Korea is Asia's fourth-largest economy.
The Constitutional Court has 180 days to rule on the legality of the impeachment, but officials said it would try to reach a decision in the quickest possible time.
Crowds gathered outside the court on Thursday and a Roh sympathiser staged a one-man demonstration demanding a fair hearing for the populist former labour lawyer. Court guards swiftly pulled down his protest banner.
The nine judges, eight men and one woman, were tight-lipped as they entered the modern wood-panelled courtroom, which was closed to reporters.
Goh Kun (C) remains acting
president until after the hearing
Delayed ruling expected
"As I've mentioned many times, we will be discussing procedures," said judge Choo Sun-hoe.
Legal experts said the court is likely to require more than a month despite the priority it would give the case, and no one expects a ruling before a general election on 15 April.
If the court upholds last Friday's impeachment, the 57-year-old Roh will be stripped of his office. A presidential election must be held within 60 days of his removal.
The members of parliament's judiciary committee, acting as prosecutors, and the president's legal representatives, have submitted legal arguments to the court.
Roh's legal team sent the court a letter arguing that the Constitutional Court rules did not require Roh's attendence but do allow him an opportunity to testify.
Public criticism of the opposition Grand National party and the Millennium Democratic party, which led the impeachment vote, have boosted the popularity of the pro-Roh Uri party in opinion polls ahead of the 15 April parliamentary election.