The call was made to the minister on Sunday night when she was in Siliguri ahead of Chief Minister Mamata Banerjee's visit, Malda police superintendent, Kalyan Mukherjee said.
The caller, sources said, claimed that he was calling Mitra on behalf of the KLO chief Malkhan Singh, who wanted the minister to pay the ransom.
Tracing the number Old Malda police had detained a woman, against whose name the number was registered.
"We are looking into the matter... We have detained one woman from Balarampur because the number from which the call was made was in her name and are investigating whether she has got any connection with the KLO," Mukherjee said.
Police arrested key KLO leaders and a Kamtapur Peoples' Party (KPP) leader following the Jalpaiguri cycle blast last December and the Assam bus firing incident last week.