President Asif Ali Zardari has cancelled his scheduled visit to Russia as a result of the ruling.
The president may convene parliament on Thursday to elect the new PM if a consensus is reached on Wednesday.
Mr Gilani's constituency has been declared "vacant" by the authorities.
The court disqualified him from holding office two months after convicting him of contempt of court.
In April, it convicted him of failing to pursue corruption charges against President Asif Ali Zardari. But it gave the PM a token sentence and spared him a jail term.
The BBC's M Ilyas Khan in Islamabad says that many in Pakistan see the court ruling as taking the clash of the institutions in the country a step further.
In an editorial, the Dawn newspaper has described the ruling as "extraordinary and unfortunate.
The paper said that the court "has both disrupted an existing democratic set-up and set a worrying precedent for the future".
Meanwhile former Pakistan Bar Council President Asma Jehangir told BBC Urdu that the government had to abide by the Supreme Court if it wanted to prevent a "soft coup".
She said that there was already a "smell in the air" to suggest that "soldiers are lurking behind a civilian face" - a reference to Supreme Court Chief Justice Iftikhar Chaudhry.
"When the court becomes a dictator, the situation could get worse than under a [military] dictatorship," she said.
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