The incident occurred yesterday in the kitchen premises of the jail, authorities said today.
According to sources, Baig assaulted Rajesh Daware following a brawl between them over an unknown issue.
Daware and his associate Arvind Abhilash Singh were sentenced to death by a Nagpur sessions court on February 4 for murdering Yug Chandak, the 8-year-old son of a doctor, on September 1, 2014.
The sources said the duo had a heated exchange which culminated into Baig thrashing Daware.
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Daware received some head injuries and was taken to the jail hospital for treatment.
The Bombay High Court had recently commuted the death sentence awarded earlier to Baig by a Pune court to life imprisonment.
Seventeen people died and over 50 were injured in the blast that happened on February 13, 2010.
Confirming the incident, Jail Superintendent Yogesh Desai told PTI that it took place yesterday and that the security staff have now placed Baig and Daware separately.
"The security outside the barracks of the inmates has been enhanced," he said.
The immediate provocation behind the incident could not be known, he added.
Meanwhile, Dhantoli Police under whose jurisdiction the prison falls were informed about the incident.
A team of police personnel, led by inspector R Mane rushed to the facility and reviewed the situation.
Police have launched an investigation to ascertain the cause behind the attack.