In London, the British foreign office called for her "immediate safe release" while Nigerian community leaders expressed outrage over the incident.
"Taking an innocent child by force is a criminal act that should be roundly condemned by Nigerians," said Anabs Saraigbe, a chieftain of the ethnic Ijaw people who are the majority in southern Nigeria.
"Such dastardly acts can't take us anywhere and must stop."
More than 200 foreigners have been kidnapped in the region since rebels and criminal gangs increased their activities against the oil industry in late 2005.
Most of the targets are foreign male employees of international companies presumed to have the resources for big ransom payments.
A witness told a local radio station that seven gunmen scared away onlookers by firing shots in the air before breaking the car windows, dragging Hill out and bundling her away in a Peugeot.
Family friends said the girl's father has been a contractor in Nigeria's oil industry for a long time and owns a bar in Port Harcourt popular among expatriate workers.
Series of kidnappings
More than a dozen foreigners are currently in captivity including five seized on Wednesday from a Shell oil rig.
Hostages are generally released unharmed after a ransom is paid, often by state governments that control huge, unregulated security slush funds, with officials taking a cut, according to industry officials.
At least two hostages have been killed in crossfire between kidnappers and security forces.
The government is trying to bring calm to the oil region where the security situation became worse after a new group emerged in late 2005 claiming to be fighting for a greater share of the oil money from the Niger Delta region.
The area remains among the poorest on the African continent largely due to corruption and financial mismanagement, despite four decades of oil production and Nigeria being the biggest producer of crude oil on the continent.