"He was taken to an unknown location and we are searching for him," the official added.
Insecurity has plagued Yemen's mostly lawless southern region in the past year, with Al-Qaeda-linked militants overrunning several towns in Aden's neighbouring Abyan province in May, and the abduction of foreigners is common.
The Saudi foreign ministry warned the kidnappers that they will be "held responsible for his (captive) safety" and demanded his immediate release.
It said the kidnappers will "achieve and get nothing out of this act," adding that the kingdom would "take all necessary measures to protect its diplomats and employees."
Another Yemeni police official told AFP that Khalidi's kidnapping was not politically motivated.
"He has some personal conflicts with people in Aden," the official said, adding that in recent months, the deputy consul had been threatened and unknown assailants had even "thrown a grenade at his home in Aden."
He did not give further details.
Late last year, unknown gunmen stopped the diplomat while he was driving in Aden, pulled him from his car and then stole it. He was unharmed.
Khalidi is the third Saudi national to be kidnapped in Yemen in as many years. In April 2011, tribesmen kidnapped a Saudi diplomat in the capital Sanaa in an apparent bid to settle a trade dispute involving a Saudi businessman.
Saeed al-Maliki, a second secretary at the Saudi embassy, was released nine days later.
In November 2010, gunmen kidnapped a Saudi doctor in north Yemen and demanded the release of nine jailed members of Al-Qaeda.
Dhafer al-Shihri, acting head of Al-Salam Hospital in Saada city, was released the same day after tribal mediation.
Saudi Arabia has played a crucial role in the power-transition deal that forced former president Ali Abdullah Saleh out of office after a year-long uprising against his rule.
The kingdom is also a key donor to the impoverished country. On Tuesday, King Abdullah ordered the donation of petroleum products to Yemen, enough to cover the country's needs for two months.
The kingdom is also expected to host a donor conference in May to organise the delivery of urgently needed humanitarian relief.
Militants with ties to Al-Qaeda have exploited the weakening central government to strengthen their presence in Yemen, launching deadly attacks against security forces, especially across the restive south and southeast.
Aden itself is also a separatist stronghold, with local militants disrupting the referendum-like presidential election last month, saying the vote failed to meet their aspirations of autonomy or outright independence for the south.
More than 200 people have been abducted in Yemen over the past 15 years, many of them by members of the country's powerful tribes who use them as bargaining chips with the authorities.
Almost all of those kidnapped were later freed unharmed.