Eight attackers opened fire on the construction site near the town of Garissa late on Sunday evening, said David Kerina, regional police chief.
“The attackers were repulsed because officers were called on time, they escaped with injuries and there are blood traces on the route they used to escape,” he said.
“We had four people who were injured during the incident and they were taken to hospital.”
National police chief Joseph Boinnet said there had been another attempted attack on a second construction camp which was also thwarted.
“We suspect that the attackers are either dead or fled with serious injuries,” he told AFP.
The attack, suspected to be the work of Somali Islamists al-Shabaab, comes less than a week after the group killed 21 people at the Dusit hotel complex in the capital Nairobi.
A suicide bomber and four gunmen with the Al-Qaeda affiliate stormed the hotel and office complex, leading to a dramatic 20-hour siege in which 700 civilians were rescued and another 28 injured.
Police have made numerous arrests in connection with the attack but are still hunting for other suspects. So far, six people have appeared court but not yet been charged.
“We have interrogated more than 30 people since the day of the attack, and some end up being suspects and some not,” a police source said.
Police on Sunday released a list of eight suspects believed to be connected to the attack, four of whom turned themselves in on Monday.