"Heavily armed individuals attacked the church... as the faithful were celebrating Sunday mass" in the town of Toulfe, the source said, adding that three people were killed.
Last week gunmen killed four Catholics in a religious procession, the day after a priest and five parishioners were murdered at mass.
Also last week, French special forces freed four foreign hostages in the former French colony during an overnight raid that cost the lives of two soldiers.
Burkina Faso's population is around two-thirds Muslim and one-third Christian.
The semi-desert country has suffered from increasingly frequent and deadly attacks attributed to a number of jihadist groups, including the Ansarul Islam group, the Group to Support Islam and Muslims (GSIM) and Islamic State in the Greater Sahara.
The raids began in 2015 in the north before targeting the capital Ouagadougou and other regions, notably in the east.
Nearly 400 people have been killed since 2015 – mainly in hit-and-run raids – according to an AFP tally.
Jihadist groups target Christian clerics as well as Muslim ones they do not consider sufficiently radical in a country where traditionally both religions have co-existed peaceably.
France has deployed 4,500 troops in Mali, Burkina Faso, Niger and Chad in a mission codenamed Barkhane to help local forces flush out jihadists.