Odinga refuses to accept the slim first-round win by Kenya's richest man, Uhuru Kenyatta, and his allies have said he plans to present a petition alleging collusion between the president-elect and the electoral commission.
Kenya's March 4 election was the first since disputes over a 2007 poll triggered tribal clashes in which more than 1,200 people were killed.
At least one person was wounded on Saturday as police quickly cleared the crowd from the front of the court building, sad a Reuters reporter at the scene.
Some of the supporters wore T-shirts marked with slogans "I support the petition" and "Democracy on trial", an echo of Odinga's statement that his petition would be a test of democracy in Kenya.
Both Kenyatta and the electoral commission deny colluding to rig the election.
(Reporting By Humphrey Malalo; Writing by Drazen Jorgic; Editing by Andrew Heavens)