Gunmen on a motorbike attacked the priest, identified only as Piero, at close range as he was riding his bicycle in the northern city of Dinajpur, before fleeing, a police inspector said.
"Riding a motorcycle, unidentified attackers shot an Italian near the Dinajpur bus station in the morning," inspector Robiul Alam told AFP by phone.
"He has been shifted to a hospital in serious condition," he said.
No one claimed responsibility for the attack and no arrests have been made.
But it bore similarities to the recent murders of an Italian aid worker who was shot dead in Dhaka in September and that of a Japanese farmer, killed in the country's north days later.
In each of those attacks, three gunmen targeted the victims while riding on a motorcycle.
The Islamic State group claimed responsibility for the killings, while the jihadists also said their militants were behind a stabbing attack on a group of police in Dhaka this month that left one officer dead.
The government has rejected the claims, insisting IS has no presence in Bangladesh, which until recently was known as a mainly moderate Muslim nation.
Police have instead blamed a banned local Islamist outfit.
Doctor working in Bangladesh
Aged in his 60s, the priest has been based at Suihari Catholic Mission in Dinajpur for more than 30 years, according to another priest, Anthony Sen, who lives in the same city.
"He is also a doctor who works at St. Vincent Hospital run by the Catholic mission and at a government hospital in the city," Sen said.
The priest was "riding a bicycle at around 8am (2am GMT) when three attackers shot him at close range", Sen said.
"One of the bullets hit his neck. He bled a lot."
Another priest, Sebastian Tudu, said the Italian also had injuries to his eyes. "Both his eyes have been bandaged. He may have been stabbed, but we are not sure," he told AFP.
Inspector Alam also confirmed the man attacked is a priest working in Dinajpur, located 350 kilometres (220 miles) north of Dhaka, close to the border with India.
Bangladesh has been reeling from rising Islamist violence in recent months, including a series of machete murders of secular bloggers and a publisher of secular books, attacks claimed by a local Islamist group.
A bombing of the capital's main Shiite shrine in Dhaka in October that left two people dead further heightened fears for minorities in the officially secular country.
Experts say Islamist militants pose a growing danger in conservative Bangladesh, warning that a long-running political crisis has radicalised opponents of the government.
Prime Minister Sheikh Hasina's government launched a crackdown on local Islamist groups after facing Western criticism this year of failing to stop the bloodshed.
The government accuses opposition groups of being behind the violence in an attempt to destabilise the country.