One explosion in the local Holiday Inn killed two people while another in a street killed a third, a local police officer who asked not to be named told AFP, adding that 12 of the injured were in a serious condition.
“Two people died at the new Holiday Inn hotel known as Kwa Chege. Another died at a Ngamia road blast,” the police officer said.
“Twenty-seven people were injured in total, 12 of them seriously and 15 sustaining minor injuries”
Asked what caused the blasts he said: “These were grenades”, adding that most of the wounded suffered shrapnel injuries.
Another police source said however that only two people were killed.
Local resident Hussein Abdi, contacted by AFP by telephone, described scenes of panic in the centre of the town where the blasts occurred, with people trying to escape from the scene of the attacks.
Garissa is the capital of Northeast province, 330 kilometres (200 miles) northeest of Nairobi. The town lies just 100 kilometres from the Somali border and 70 kilometres from Dadaab, a complex of Somali refugee camps.
Nairobi sent troops and tanks into neighbouring Somalia in mid-October to fight Islamist insurgents who it accuses of staging a series of attacks on Kenyan soil.
Since the deployment, the northeast of the country has been the focus for a series of attacks blamed by Kenyan authorities on sympathisers of the Shebab Islamist insurgency which controls large areas of central and southern Somalia.