The letter contained an "unconditional apology" from Hussain, who said he was putting himself at the mercy of the court.
Hussain, who has lived in self-exile in London since 1992, said he had complete faith in rule of law and respected the judiciary.
He further said he wanted to withdraw his remarks against the judiciary and would not make such comments in future.
The apex court accepted the apology and dismissed the notice issued to Hussain.
The Chief Justice said that if Hussain respected the judiciary, the apex court too respected him.
Earlier, the MQM's legal team had asked the bench to excuse Hussain from having to appear personally in court due to security concerns.
The Supreme Court had issued a notice to Hussain on December 14 to explain why action should not be taken against him under the contempt of court law for his remarks about the judiciary.
The court had also directed Hussain to appear in court in person today.
The apex court had observed that Hussain had used language that came under the purview of the contempt of court law.
It further contended that Hussain was interfering in the work of the apex court and spreading hatred against the judiciary.
During a telephonic address to a gathering in Karachi on December 2, Hussain had taken exception to the apex court's observations about the delimitation of parliamentary constituencies in Karachi, Pakistan's largest city that is a stronghold of the MQM.
Hussain had described certain remarks by judges as "unconstitutional" and "undemocratic" and claimed they amounted to contempt for the mandate given by the people of Karachi.
The MQM chief frequently addresses public meetings and gatherings across Pakistan by telephone.
Despite being based in London, he continues to maintain a firm grip on the MQM, which is a key partner in Pakistan's ruling coalition.
Islamabad: The MQM's legal team presented a letter signed by Hussain to a three-judge bench led by Chief Justice Iftikhar Chaudhry, which was hearing the case.
First Published: Monday, January 07, 2013, 18:41