About 10 gunmen crossed from Somalia to abduct the workers from the border town of Mandera.
Residents said two of the staff were from Zimbabwe and Pakistan, while the third was listed as European.
Kidnappings are not uncommon in the region and most of the people abducted are released unharmed.
Two French hostages were seized earlier this week in Somalia’s capital, Mogadishu, and have been handed to a Somali Islamist group.
In the latest incident, the three aid workers were taken from their office in Mandera, in north-eastern Kenya.
The country director for Action Against Hunger confirmed there had been an incident but would not give details.
Two Frenchmen were seized from this Mogadishu hotel on Tuesday
Aid workers and journalists are particular targets for kidnappers and are often released after ransoms are paid.
One official told Associated Press that a security guard had been shot in the head during the abduction and was being treated in hospital for "life-threatening injuries".
The two French hostages have reportedly been handed to the al-Shabab militant group, which has carried out public executions.
A source in the Somali presidency said: "If they are in the hands of al-Shabab it is very, very serious".
The two security advisers, who were training government troops, were seized from a Mogadishu hotel on Tuesday.
The BBC’s East Africa correspondent, Will Ross, says the kidnappings are a result of the general lawlessness in war-torn Somalia.
But he says even in the Kenyan capital, Nairobi, there has been a spate of kidnappings in recent weeks – all for ransom.
Somalia has not had a functioning national government since 1991.
Moderate Islamist Sheikh Sharif Sheikh Ahmed was sworn in as president in January after UN-brokered peace talks.
He promised to introduce Sharia law but hardliners accuse him of being a Western stooge.