A BBC correspondent in Karachi says the situation is tense but peaceful. Most shops and schools are closed.
Last month, more than 80 people were killed in clashes in the city after the killing of another MQM politician.
The MQM has long been accused by its critics of illegal activities, and of endorsing or ignoring ethnic, sectarian and political violence in Karachi.
British police say no-one has yet been arrested over the stabbing of Mr Farooq, and it is not clear if it was politically motivated.
Raza Haroon, a member of the MQM central coordination committee, said: "He was a gentleman, a very, very soft spoken person with a lot of knowledge, and who was very outspoken as well.
"It's a very huge loss to the party to have lost a senior leader, in such a manner. This is an irreparable loss and a great tragedy for the MQM," he added.
'Great loss' Mr Farooq had been living in exile in the UK since 1999, when he claimed asylum. He had previously spent seven years on the run from Pakistani police, who accused him of involvement in several serious crimes.In 1999, he told the BBC the charges against him were politically motivated.
The former Pakistani parliamentarian was one of the founding members of the MQM, a former opposition party which is now part of the ruling PPP-led alliance.
After news emerged that he had been stabbed several times in the head and neck, the MQM declared a 10-day mourning period in Pakistan and in its offices across the world.
Prime Minister Syed Yousuf Raza Gilani said the PPP would also suspend its activities for 10 days, adding: "It was a great loss to the party and the family."
MQM leaders said they expected Mr Farooq's body to be flown back to Karachi for burial after legal formalities had been completed.
Local media in Karachi reported that some vehicles were torched and shots fired late on Thursday, but police said there had been no violence on Friday as hundreds of party activists converged on his family home.
Amid fears that the crowd could turn violent, most markets, restaurants and schools were closed and no public transport was available.
The BBC's Shoaib Hasan in Karachi says MQM leaders had told him there was "a lot of grief and a lot of sorrow going around".
But, our correspondent says, the situation has remained peaceful.
Mr Farooq was in essence the party's deputy leader, though he had not returned to Pakistan since claiming asylum in the UK, he adds.
Dozens of people were killed and hundreds were wounded in several days of clashes in Karachi last month, sparked by the killing of an MQM parliamentarian, Raza Haidar. He was shot dead while attending a funeral.Most of those killed belonged to the Pashtun community, whom MQM leaders had initially held responsible for the attack. Investigators later said the pro-Taliban militant group, Lashkar-e-Jhangvi, was behind it.
MQM activists were also involved in bloody factional clashes and battles with the security forces in Karachi during the 1990s.
The MQM seized power in Karachi in the 1980s. The party claimed to represent ordinary working class people, but opponents accused it of kidnap, torture and murder.
In 1992, the authorities launched Operation Clean Up - in the next six years some 8,000 people were killed and Mr Farooq fled to London.