Police and security officers are said to have arrived at 6am local time on Tuesday in nine police vans and rounded up 15 women and 22 men.
They were detained and charged with "breach of the peace, public nuisance and obstruction of a public servant during the course of his duty" offences. Twenty of the accused received fines, with 17 others acquitted of all charges against them.
According to anti-persecution organisation, Christian Solidarity Worldwide, Tuesday's raid is one of a series of actions taken against the Bahri Evangelical Church in recent weeks.
On 17 November, security personnel arrived at the church and demolished a wall of the main building and neighbouring houses. Security personnel presented the church leaders with a court order demanding that the property be given to a Muslim businessman who was the alleged owner.
On 18 November, the church leaders filed a formal challenge over the legal ownership and are awaiting a court decision.
On the same day, security personnel arrived with a second court order requiring that all property be removed from one of the houses and padlocks belonging to the Muslim businessman fitted on all doors. Church members formed a human shield preventing the security personnel from interfering with the property.
On 25 November, eight people were arrested for refusing to comply with the court orders to hand over the church to the Muslim businessman.
Local sources report that police officers are still surrounding the church, indicating their intention to take further action, according to CSW.
The raid on Khartoum Bahri Evangelical Church is the third incident of the government destroying church buildings during 2014, which Christian Solidarity Worldwide says indicates an escalation of intimidation against Christians.
CSW Chief Executive Mervyn Thomas said: "We are deeply concerned by the continuing action of the Sudanese authorities against the Khartoum Bahri Evangelical Church.
"The destruction of a religious building is a violation of congregant's rights to freedom of religion or belief as guaranteed in article 6 of the Sudanese constitution."