Police said militant was arrested during a raid in Orangi Town area of Karachi.
Islam was a "most wanted" commander of the Taliban faction and was linked to cases of kidnapping, extortion, robberies and targeted killings, SSP Farooq Awan said.
"We are interrogating him to find out about the presence of the Punjabi Taliban in Karachi," Awan said.
The arrest of Islam was made during an operation against terrorists and criminals operating in Karachi.
The Punjabi Taliban came into focus after the faction attacked the Sri Lankan cricket team in Lahore in March 2009, an incident which led to the isolation of Pakistan by other cricket-playing countries.