A security source told the agency that the attack was carried out by a "group of armed men estimated [to number] between twenty and thirty".
Former colonial ruler France has deployed 4,500 troops in Mali, Burkina Faso, Niger and Chad in a mission codenamed Barkhane to help local forces flush out jihadist groups.
"They burned down the church, then shops and a small restaurant before going to the health centre where they searched the premises and set fire to the head nurse's vehicle", Zongo added.
The attacks started in the north of the country before targeting the capital Ouagadougou and other regions, notably the east of the country.
"The city is filled with panic".
Over 350 people have been killed in the raids which have been attributed to a number of jihadist groups, including the Islamic State in the Greater Sahara and the Ansarul Islam group.
Religious leaders are not the only people targeted by the extremists.
The attack came two days after the release of two hostages in Burkina Faso during a daring French special forces military operation that resulted in the deaths of two of their own soldiers.
Frenchmen Laurent Lassimouillas, 46, and Patrick Picque, 51, were seized by kidnappers in Benin's Pendjari National Park, near the border with Burkina Faso, on May 1.
Burkina Faso is part of the vast Sahel region, which has turned into a hotbed of violent extremism and lawlessness since chaos engulfed Libya in 2011. It follows a similar attack on a Christian church last month.
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