President Robert Mugabe has been placed under house arrested by the military, marking the likely end of his decades-long rule.
Most Rev Chad Gandiya said: "We are concerned that whatever changes are in store for us, these take place in a peaceful manner."
Mr Mugabe is reportedly being kept with his wife and a number of advisors, while the military has maintained a presence on the streets of Harare.
Bishop Chad said: "The situation is still unfolding and so people can speculate... but I think the reality is that the army is definitely in control."
South African ministers arrived in the Zimbabwean capital on Thursday for talks involving military figures and Mr Mugabe who, at 93 years old, is the world's oldest head of state.
Describing the mood in the city, Bishop Chad said: "People are going about their normal duties but obviously people are a little bit sensitive to the situation but we thank God that there is calmness."
Meanwhile, bribe-seeking police officers have vanished from roadblocks in Harare and trade unions have urged people to go to work as usual.
Mr Mugabe has been urged to resign peacefully by more than 100 civil society groups, who also called for the constitution to be respected.
Click here to listen to Bishop Chad Gandiya speaking with Premier's John Pantry and Rosie Wright: