"Islamabad High Court judge Noorul Haq Qureshi was on leave today therefore the hearing of the case could not be held," Lakhvi's counsel Raja Rizwan Abbasi told reporters.
He said the court office would fix the next date of hearing.
Lakhvi on Tuesday had challenged his 'fresh' detention under Maintenance of Public Order.
"The government has detained me on illegal grounds. After bail from the trial court, the government had no legal justification to put me behind the bar. The government is doing so only on the pressure of India," the petition said.
On December 18, 2014, the trial court granted bail to 54-year-old Lakhvi but was detained the next day under the Maintenance of Public Order (MPO).
However, the IHC suspended Lakhvi's detention on "weak legal ground". Just before he was to be released from Adiala Jail, Rawalpindi, Lakhvi was arrested on charges of kidnapping an Afghan national in 2009.
Pakistan faced strong reaction from India following the bail order.
He has been kept in the high-security Adiala Jail, Rawalpindi till second week of the next month under the same order after the Pakistan government extended his detention by 30 days.
Earlier in January, Lakhvi had challenged his detention in the High Court which suspended the detention order. However, the Supreme Court set aside the High Court's order on the government's plea.
Lakhvi and six others - Abdul Wajid, Mazhar Iqbal, Hamad Amin Sadiq, Shahid Jameel Riaz, Jamil Ahmed and Younis Anjum - have been charged with planning and executing the Mumbai attack in November, 2008 that left 166 people dead.
All of them are kept at the Adiala Jail.