Clooney is part of the high-profile legal team representing Nasheed. Her visit to the honeymoon island comes days after his local lawyer Mahfooz Saeed was stabbed by an unknown attacker.
"I'm here unfortunately at a time when the human rights situation and security situation is deteriorating day by day," the private Maldives Independent website quoted her as saying at the airport.
Nasheed, who was elected president in 2008, was sentenced in March under a tough anti-terror law, after a widely-criticised trial that the United Nations, Washington and others said was deeply flawed.
Clooney and her Washington-base co-counsel Jared Genser are expected to travel this week to the high-security Maafushi prison island where Nasheed is being held, although it remains unclear whether they will be allowed to visit him.
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Nasheed, the country's first democratically-elected leader, was toppled in February 2012 after a mutiny by police and troops that followed weeks of protests over the arrest of a top judge.
He was convicted in March for ordering the judge's detention while he was still president, charges which his Maldivian Democratic Party (MDP) described as politically motivated.
Members of the opposition MDP met Clooney, a respected human rights lawyer who shot to international stardom when she married actor George Clooney, when she arrived at the airport today.
They arranged a traditional welcoming party of drummers and dancers.
Nasheed announced in April that Clooney would be part of his international legal team, along with Genser -- who has previously represented Myanmar's Aung San Suu Kyi -- and Ben Emmerson, a judge on war crimes in Rwanda and the former Yugoslavia.