Mohamed Nasheed, who became the country's first democratically elected leader, led the Sept. 7 first round with more than 45 percent of the vote, but failed to muster the 50 percent needed to win. He was to face Yaamin Abdul Qayyoom, a brother of the country's longtime autocrat, Maumoon Abdul Gayoom, in the runoff.
Qasim Ibrahim, who finished a close third, challenged the result, claiming a flawed voter registration list.
Hundreds of supporters from Nasheed's Maldivian Democratic Party demonstrated in the capital, Male, on Friday demanding that the election be held as scheduled.
"The Supreme Court has lost all credibility in the eyes of Maldivians and the watching world," MDP spokesman Hamid Abdul Ghafoor said in a statement.
Soon after Friday's court order, police cordoned off the election office. Police spokesman Hasan Hanif said they were protecting the building from harm by those disappointed by the postponement.
In recent days there has been increasing international concern over the country's young democracy.
The United States, the United Nations, Australia and India have all praised the conduct of the first round of the election. The European Union has asked that the runoff election be held according to schedule.
The country held its first-ever multi-party election in 2008 after Gayoom's 30-year autocratic rule.