The Interior ministry said at least 79 people were injured by the attackers and had been rushed to a hospital with nine in critical condition.
Two officers and a civilian were airlifted to Nairobi for treatment.
The gunmen are said to have attacked the institution around 5.30am on Thursday.
Unconfirmed reports say that students may have been taken hostage.
Nation.co.ke reporter Abdimalik Hajir said he saw the bodies of the guards near the university’s main gate.
Inspector-General of Police Joseph Boinnet said there was a shootout between the attackers and police officers who were guarding the students’ hostels.
“The attackers shot indiscriminately while inside the university compound.
Students run out of Excel Secondary School, located next to Garissa University College, after they were ordered to leave following an attack at the college on April 2, 2015. PHOTO | ABDIMALIK HAJIR | NATION MEDIA GROUP
“However, the attackers retreated and gained entry into the hostels. … (A) joint force composed of NPS officers and other security agencies arrived and are engaged in an elaborative process of flushing out the gunmen from the hostels,” he said in a statement posted on his Twitter account.
KDF and police have entered the university’s compound.
Following the attack, the Somalia-based Al-Shabaab militant group claimed responsibility for the attack.
Terrified students rescued from the college were gathered at a KDF camp near the Garissa airstrip.
In the meantime, Mr Boinnet, who flew to Garissa following the attacks, urged Kenyans to remain calm as security authorities dealt with the situation.
He was accompanied by the Interior Cabinet Secretary Joseph Nkaissery and Garissa Township MP Aden Duale.
At the same time, students who were seriously injured were flown to Nairobi for treatment.
In a tweet, Kenya’s Interior Ministry said one of the attackers had been arrested as he tried to flee from the scene.