The airport and Houthi officials, speaking on condition of anonymity because they were not authorised to speak to reporters, said the six are flying to the Gulf nation of Oman, which negotiated their release.
The officials said the hostages, who were detained earlier this year, are three Americans, two Saudis and a British national. The identities of the hostages were not immediately known.
Officials from the Houthi media centre refused to explain why they had detained the hostages. But at least one of them is a journalist, whom they said "entered the country illegally" and "worked without notifying the authorities."
Meanwhile, Houthi spokesman Mohammed Abdel Salam held a press conference at the airport and refused to confirm the hostages' release.
"If we were to release anyone, it would be in exchange for the release of Houthis," he said, without specifying which authorities he was addressing.
The conflicting information could not immediately be reconciled.
Meanwhile in the western province of Ibb, the Saudi-led coalition's airstrikes against a Houthi stronghold and prison facility killed 11 and wounded more than 50 rebels and civilians, security officials and witnesses said.
Today's airstrikes hit a security directorate where the rebels held more than 300 prisoners underground, said the officials, who remain neutral in the conflict that has splintered the country's security forces.
Many managed to escape, but dozens remain buried under the rubble, they added.
Many of the confirmed dead, witnesses said, were onlookers who had gathered around the building following the first strike, only to be hit by the second.
All officials and witnesses spoke on condition of anonymity because they are not authorized to brief reporters.
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