Media reports said at one church, a woman with a younger child and a teenager was being questioned by security when the bomb exploded.
Police have confirmed the explosions all occurred within 10 minutes of each other.
Frans Barung Mangera, East Java police spokesman said: “The victims are being identified.”
He added: “We have confirmed one died at the scene, one died at the hospital, two police officers were injured and there are some civilians injured.
“In total 13 people are being treated at the hospital.”
A bomb exploded at church in Indonesia’s Surabaya City in East Java
The incident is believed to have happened around 7am local time
The number of fatalities is expected to rise.
Footage seen by Express.co.uk show a number of dead bodies.
People at the scene desperately tried to help the injured.
Television images showed toppled motorcycles and debris scattered around the entrance of one church.
Police have since cordoned off the areas as crowds started to gather.
Authorities are also investigating whether there was an explosion at a fourth church.
Police ordered the temporary closure of all churches in Surabaya, and a large food festival in the city was cancelled.
The attack happened in Indonesia’s second biggest city.
Surabaya is a port city on the Indonesian island of Java with a population of around 2.7million.
Police are currently at the scene
The bombings come just days after Islamist militant prisoners killed five members of an elite counter-terrorism force during a 36-hour standoff at a high-security jail on the outskirts of the capital, Jakarta.
In January 2016 four suicide bombers and gunmen attacked a shopping area in central Jakarta.
In the early 2000s, Indonesia was rocked by terrorist attacks by affiliates of al Qaeda, including a bomb attack in Bali that killed 202 people, many of them foreign tourists.
The police said the number of fatalities is currently not known
Police cordoned off areas as crowds gathered