"The tunnel is about 12 metres (39 ft) long and we suspect it took more than a week to build," the head of Kerobokan prison Tony Nainggolan said, adding that police believed the men were still in Bali and not far from the prison.
The four are Australian Shaun Edward Davidson, Bulgarian Dimitar Nikolov Iliev, Indian Sayed Muhammad Said and Malaysian Tee Kok King, Bali police spokesman Hengky Widjaja said.
The tunnel had a diameter of 50 x 75 cm (20 x 30 inches) and was found filled with water today morning, Widjaja said.
Kerobokan houses a fairly large number of foreign inmates, given Bali's status as an international holiday destination and transport hub.
The four men were serving sentences for different crimes, from immigration rules violation to drug crimes, Widjaja said.
The head of the prison said that 10 guards were on duty on Sunday night when the escape is believed to have taken place.
Indonesian prisons are frequently overcrowded and a war on drugs being led by the government of President Joko Widodo has triggered a spike in the number of convicted drug offenders, stretching an already overwhelmed jail system.
The capacity of Kerobakan is 323 inmates, but it currently houses more than four times that number at 1,378, according to government data.
Prison escapes are fairly common in Indonesia and authorities launched an investigation last month after around 350 inmates broke out of an overcrowded jail on Sumatra island in Riau Province.