Police confirmed that an Italian national, 23, had been abducted from the town of Chakama in the drought-ridden coastal region of Kilifi, where she had been working for the NGO Africa Milele Onlus.
The group, which was set up in Italy, run a number of aid projects on the continent.
She was taken after dark on Tuesday evening, with the attackers firing “indiscriminately at residents” with AK-47 assault rifles during the raid.
All of those wounded were under 25 – including a 10-year-old shot in the eye and a 12-year-old hit in the thigh – and required hospital treatment.
Police chief Joseph Boinnet said investigators had not yet determined who was responsible for the attack, nor what the motive was, but previous kidnappings of foreigners on the coast have been blamed on Somali Islamic militants.
In 2011, Kenya sent troops into the neighbouring country to fight the al-Shabab group in response to the abduction of four foreign nationals, one of whom was a cancer-stricken French woman who died in captivity.
Wheelchair-bound Marie Dedieu, 66, was snatched in the middle of the night from her resort island home near Lamu seven years ago and her kidnappers did not provide her with the daily medicine she needed.
The spate of abductions led to fears for the Kenyan tourism industry.
Al-Shabab, which has links to al Qaeda, has since carried out further attacks in Kenya, saying it is vengeance for the presence of troops in Somalia.