According to police, both of them are lodged in the jail as undertrials.
Gopal Shetty (35), an accused in the Maharashtra Control of Organised Crime Act (MCOCA) was allegedly assaulted by Salim Faizal Khan, who had been arrested in an attempt to murder case registered against him at Nirmal Nagar police station.
"Shetty was assaulted by Khan following a heated argument between them. Both of them suffered injuries in the ensuing scuffle," said a senior police officer.
"Arthur Road Jail is a high-security prison and efforts are being made to ensure that such incidents do not take place in future again," the officer said.
Investigations in the incident are on and appropriate action will be taken after the probe, he said.
On May 31, a scuffle broke out between two groups of prisoners in the Arthur Road Jail, leaving five of them injured.