Locals rushed to the church after hearing the blast as scuffles erupted with police.
A police car was torched as protesters tried to surge past police to try to get at the man and two women who attacked the church.
Large numbers of police were deployed to the church to try to rescue the attackers who had taken shelter inside.
The man was injured in the incident and two ambulance workers were trapped inside for hours after protestors stopped them from leaving.
Police later removed the three and took them away for
questioning.
They described the man as “peculiar” and said he suffered from severe financial hardship.
Internal Security Minister Gideon Ezra said it was not a terrorist attack and the incident was prompted by personal grievances.
Officials say the church was undamaged.
Israeli TV broadcast images showing police hitting some people with batons, with at least two tear gas grenades thrown.
Christians believe the church is where the Angel Gabriel told Mary she would become the Mother of Jesus.