The judge issued the order after reviewing evidence produced by investigative agency against them, the sources were quoted as saying, PTI reported.
The judge recorded the suspects' statements before sending them to physical remand, the report said.
Meanwhile, 'Dawn' on Sunday reported, quoting an unnamed security official, that the suspects, including Lakhvi, were produced before judge Sakhi Mohammed Kahut of the anti-terrorism court at an undisclosed location.
The FIA is expected to submit a chargesheet against the suspects at the end of the remand, it said. The agency has already conducted preliminary investigations into the case.
Lakhvi, the alleged mastermind of the Mumbai attacks, was arrested in December near Muzaffarabad, the capital of Pakistan-occupied Kashmir.
Both Lakhvi and Shah, another accused named in the FIR is Hamad Ameen Sadiq, a key militant linked to the Lashkar-e-Taiba, western diplomatic sources told news agencies.
Pakistan on Saturday briefed foreign envoys on the steps taken by it to cooperate with India in bringing the perpetrators of the Mumbai attacks to justice and to eliminate terrorism and militancy.
The heads of diplomatic missions in Islamabad were also briefed by foreign secretary Salman Bashir on Pakistan's perspective on "peace, security and stability, with particular emphasis on the situation in South Asia".
Meanwhile, Pakistan interior minister Rehman Malik on Saturday said that his country may demand from India the custody of Ajmal Kasab, the lone survivor among the accused of the Mumbai terror attacks.
"So far, we have not asked India for the custody of Kasab. But we may seek it if the investigation demands," Rehman Malik said in the southern port city of Karachi, adding that at the moment, it would be premature to say anything else in the matter.
India was quick to react, saying there was no way this could happen.
"The crime was committed in India. There is no question of handing Kasab to them. In fact, Pakistan should hand over to India the other suspects they've arrested because they were responsible for this terror attack. It can't be the other way around," sources in the Indian external affairs ministry said in New Delhi.
"On what basis do we send Kasab out there? The crime was committed out here (in Mumbai), therefore logic and reasoning demands that the suspects who they've rounded up be sent here (to India)," the sources told IANS.
Special public prosecutor Ujjwal Nikam said the state had gathered enough evidence to show that Kasab, the only surviving November 26 Mumbai terror suspect, had been a part of the criminal conspiracy hatched in Pakistan to orchestrate the terror strikes at pre-decided sites in Mumbai.
"We have all the evidence required. The chargesheet will be filed within a couple of days," Nikam said.
"He is not educated and (is) poor and the concept of religion was wrongly projected to him," he said.
IANS reported that Nikam said while victims of such systematic brainwashing by extremist forces needed proper handling, there was a need to distinguish between a freedom fighter and a terrorist.
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