On Thursday, the Vatican had temporarily "relieved him" of his pastoral duties even though the Bishop had earlier announced this week that he was stepping down to concentrate on fighting the case levelled against him.
A protesting nun said they were all waiting for the news of the arrest of the bishop so a strong message goes out to those who abuse women.
On Wednesday, police questioned him for 7 hours.
In a letter, Apostolic Nunciature in India said "The Holy Father has received the request of Rt".
When asked whether Mulakkal can be arrested before September 25, the day his anticipatory bail plea will come up for hearing in the high court, the top police officer said, "I think, legally there is no problem".
There was no immediate comment from Bishop Franco Mulakkal or his lawyers - though he has denied the charges in interviews in the past.
The Bishop was accused of repeatedly sexually assaulting a nun for two years between 2014 and 2016. The nun filed a police complaint against Mulakkal after his public relations officer, Fr Peter Kavumpuram, filed a complaint against her brother alleging that he had threatened to kill the bishop.
Mr Sankar told reporters on Friday that the police would now investigate charges of rape, illegal confinement, unnatural sex and intimidation. He is the bishop of the northern Indian city of Jalandhar. "It is the first victory in our struggle against the Bishop".
The news was welcomed by people in Kochi where nuns of various churches have been protesting for the past ten days. When the church failed to take action on this matter, the nun approached the Kerala police.
The case comes at a time when the Christian community, which accounts for 19 percent of the state's population, is reeling under an erosion of trust as sexual abuse cases involving the clergy pile up.