Dr Balvinder Mehat is accused of carrying out a nontherapeutic circumcision or a procedure for religious rather than medical reasons on the three-month old baby believed to belong to the Muslim faith in July 2013.
Nottinghamshire Police had initially turned down the case for insufficient evidence to bring criminal charges. However, earlier this week, the force agreed to re-investigate the case and made two further arrests besides 61-year-old Dr Mehat on Wednesday.
"A 61-year-old man was arrested on suspicion of grievous bodily harm with intent. A 44-year-old man and a 47-year-old woman were arrested on suspicion of conspiracy to commit grievous bodily harm. They have all been released pending further investigation. Our enquiries are ongoing," Nottinghamshire Police said.
"Where a victim or member of the public feel a decision made by us to discontinue an investigation should be reviewed, we will always welcome an appeal," it added.
It is unclear whether the GP, who is based at Bakersfield Medical Centre in the city of Nottingham, had been told that the boy's parents had consented.
The couple are separated and the procedure is believed to have taken place when the boy was with his father's family.
The police enquiry was reopened this week after protests by campaign group Men Do Complain, which fights against circumcision, and Saimo Chahal, a human rights lawyer.
"The mother did not consent to her son undergoing the circumcision procedure, which could constitute a criminal offence. While some people with religious beliefs see circumcision as normal, there are others who see it as an unnecessary assault which can be physically and psychologically harmful," Mr Chahal said.
The baby boy is now aged four and suffers from a number of recurrent problems, including inflammation and infections, as a result of the circumcision, according to his mother, who is also considering legal proceedings against the GP.
"He was screaming and crying, but trying to comfort him just disturbed the wound and made it worse. I could not believe what they had done to him. He has been mutilated and suffered permanent damage," the 26-year-old unnamed mother said.
"Circumcision is a barbaric, torturous ritual that takes place on innocent boys without their consent," she added.
The mother has also complained to the UK doctors' watchdog, the General Medical Council (GMC), which is carrying out an investigation.
Guidelines from the British Medical Association state that both parents should give consent for the non-therapeutic or "ritual" circumcision of children.
If parents disagree, a doctor may only proceed with permission from a UK court. Children old enough to express their opinion should be consulted, and their wishes must be taken into account.
Circumcision is widely practised in both the Jewish and Muslim faiths around the world.
Dr Mehat is yet to make a comment, saying that it would not be appropriate while investigations are ongoing.