Imran Farooq was killed on Thursday but it was not clear if it was politically motivated.
Most shops and schools were closed and no public transport was available after the MQM announced 10 days of mourning. A few vehicles were torched, police said.
All petrol pumps and CNG stations had been shut down after the incident.
“We are confident that the culprit will be arrested and will be given exemplary punishment,” Farooq Sattar, a senior member of the MQM and a federal minister, told reporters in Karachi.
Sattar refused to speculate on the motives behind the killing, saying they were awaiting results of British investigations.