Priest Reji Yohanan, vicar of St Peters Church at Thuvayoor South, and church's trustee Suraj and secretary Mathew were those arrested, they said.
They were later released on bail, police said.
This is the second such instance of an arrest of a church priest for conducting a funeral with large people in attendance in Kerala since the government imposed curbs to contain the spread of the deadly virus.
Over 50 people participated in the funeral service held at 11 am at the St Peters church complex amid the complete lockdown in the state.
A case has been registered against the three persons under section 188 (disobedience of government order) of the Indian Penal Code and the Kerala Police Act section 118E (causing danger to the public), police said.
On Monday, a priest, who conducted a holy mass at a church in Chalakudy in which over 100 people took part, was arrested.
He was also later let off on bail.
Pathtanamthitta has reported 10 cases of the virus as on Wednesday. On March 25, the Chief Minister, in his daily press briefing confirmed that 2 cases have been reported positive in the state. The first few cases from Pathanamthitta belonged to the family who had returned from Italy and had tested positive for the virus and a few of their family who had been the family's primary contacts.
Kerala reported 9 new cases of the novel coronavirus on Wednesday. However, Chief Minister Pinarayi Vijayan confirmed that 6 patients who had tested positive and was in isolation in the state has now recovered. The total active cases of SARS-CoV2, which causes the COVID-19 disease, in Kerala is currently 112.