The attack follows a further two incidents with two foreigners last week in the country, which is predominantly Muslim.
Islamic State (IS) claimed responsibility for the attacks last week - one on a Japanese agricultural worker and the other on an Italian aid worker.
But the government says IS are not operating in Bangladesh and has blamed the opposition for trying to destabilise the country.
52-year-old Pastor Luke Sarker, suffered minor injuries when three men aged 25-30 attacked him with a knife at his home in the north-western district of Pabna, said the area's senior police official, Siddikur Rahman.
Mr Sarker, the pastor of Faith Bible Church, said the men had phoned him around two weeks previously saying they wanted to visit him to learn about Christianity.
But it has been reported that after they arrived they tried to slit his throat with a knife.
Mr Sarker's wife came to his rescue and the men fled.
Police have recovered a motorbike from outside his home.
Police officer, Mr Rahman, said there are no clues yet about the identities of the three men but suspect they could be members of a fundamentalist group.
Bangladesh has been struggling in recent months with a rise in violence claimed by hard-line Islamic groups, banning several that have been blamed for killing four secular bloggers this year.
Speaking on Premier's News Hour Manoj Raithatha from the South Asian Forum of the Evangelical Alliance said: "It's sad to say that in Bangladesh, a country where there's been relative peace in that country, is now being impacted as well by the rise of various Islamic groups.
"There seems to be tensions between religious groups that weren't there before.
"And I think what we're seeing is the overspill aren't we of what is happening in the Middle East, in central Asia, is having an impact globally."
Listen to Premier's Hannah Tooley speak to Manoj Raithatha from the South Asian Forum of the Evangelical Alliance here:
