Revd. Ian Hadfield told Premier it was initially feared a Dutch national attending All Saints Church had died in the suicide bombs and shootings.
He says it later emerged the man had been taken to hospital for an operation.
Speaking on Premier Christian Radio's New Hour programme, Revd. Hadfield said: "The wife, [is] very upset and sad but, at first, she couldn't make contact with her husband and we were being told that he'd actually been killed. So, [being] in hospital, having an operation is much better than the first news we'd heard.
"Go to a shopping mall, you'll normally have your bag checked. Go to a hotel, your car would be checked underneath. You'll walk through metal detectors into hotels and into shopping centres, as well. [The authorities] will be, I guess, more vigilant than they have been in the past. Jakarta has known bombs before.
"At our church, in Christmas Eve 2000, we had a bomb left here but, thankfully, it didn't go off. So, even our church is used to having increased security."
A Dutch Foreign Ministry spokeswoman has said a Dutch man was seriously injured and was undergoing surgery.
Attackers targeted a Starbucks cafe on Thamrin Street, in an area popular with shoppers, leaving at least seven people dead and 20 others injured.
An Indonesian, a Canadian and five attackers died in the incident which was watched by office workers from nearby high-rise buildings.
Police said the incident mimicked November's terror attacks in Paris and was linked to the Islamic State group.
The Aamaq news agency, which is affiliated with Islamic State, is quoting an annonymous source as saying the group is responsible for the violence.
It was around the same time when two other suicide bombers killed themselves and an Indonesian man at a nearby traffic police booth.
Minutes later, two gunmen attacked a group of policemen but, after a 15-minute gunfight, both attackers were killed, police say.
It was the first major attack in Jakarta since the 2009 bombings of two hotels which killed seven people and injured more than 50.
Before that, bombings at nightclubs on the island of Bali killed 202 people in 2002.
Speaking on television, Indonesia's President, Joko Widodo said:
"This act is clearly aimed at disturbing public order and spreading terror among people.
"The state, the nation and the people should not be afraid of, and be defeated by, such terror acts."